RD Sharma Maths Solutions Class 9

RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.2

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.2

Question 1.
Write the following in the expanded form:

Solution:

Question 2.
If a + b + c = 0 and a² + b² + c² = 16, find the value of ab + be + ca.
Solution:
a + b+ c = 0
Squaring both sides,
(a + b + c)² = 0
⇒ a² + b² + c² + 2(ab + bc + ca) = 0
16 + 2(ab + bc + c) = 0
⇒ 2(ab + bc + ca) = -16
⇒  ab + bc + ca =-\(\frac { 16 }{ 2 }\) = -8
∴ ab + bc + ca = -8

Question 3.
If a² + b² + c² = 16 and ab + bc + ca = 10, find the value of a + b + c.
Solution:
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
= 16 + 2 x 10
= 16 + 20 = 36
= (±6)²
∴ a + b + c = ±6

Question 4.
If a + b + c = 9 and ab + bc + ca = 23, find the value of a² + b² + c².
Solution:
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ (9)² = a² + b² + c² + 2 x 23
⇒ 81= a² + b² + c² + 46
⇒  a² + b² + c² = 81 – 46 = 35
∴ a² + b² + c² = 35

Question 5.
Find the value of 4x² + y² + 25z² + 4xy – 10yz – 20zx when x = 4, y = 3 and z = 2.
Solution:
x = 4, y – 3, z = 2
⇒ 4x² + y² + 25z² + 4xy – 10yz – 20zx
= (2x)² + (y)² + (5z)² + 2 x2 x x y-2 x y x 5z – 2 x 5z x 2x
= (2x + y- 5z)²
= (2 x 4 + 3- 5 x 2)²
= (8 + 3- 10)²
= (11 – 10)²
= (1)² = 1

Question 6.
Simplify:
(i)  (a + b + c)² + (a – b + c)²
(ii) (a + b + c)² –  (a – b + c)²
(iii) (a + b + c)² +   (a – b + c)² + (a + b – c)²
(iv) (2x + p – c)² – (2x – p + c)²
(v) (x² + y² – z²)² – (x² – y² + z²)²
Solution:

Question 7.
Simplify each of the following expressions:

Solution:

Hope given RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.2 are helpful to complete your math homework.

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RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1

Question 1.
Evaluate each of the following using identities:
(i) (2x –\(\frac { 1 }{ x }\))²
(ii)  (2x + y) (2x – y)
(iii) (a²b – b²a)²
(iv) (a – 0.1) (a + 0.1)
(v) (1.5.x² – 0.3y²) (1.5x² + 0.3y²)
Solution:

Question 2.
Evaluate each of the following using identities:
(i) (399)²
(ii) (0.98)²
(iii) 991 x 1009
(iv) 117 x 83
Solution:

Question 3.
Simplify each of the following:

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.
If 9x² + 25y² = 181 and xy = -6, find the value of 3x + 5y.
Solution:
9x² + 25y² = 181, and xy = -6
(3x + 5y)² = (3x)² + (5y)² + 2 x 3x + 5y
⇒ 9X² + 25y² + 30xy
= 181 + 30 x (-6)
= 181 – 180 = 1
= (±1 )²
∴ 3x + 5y = ±1

Question 8.
If 2x + 3y = 8 and xy = 2, find the value of 4X² + 9y².
Solution:
2x + 3y = 8 and xy = 2
Now, (2x + 3y)² = (2x)² + (3y)² + 2 x 2x x 3y
⇒  (8)² = 4x² + 9y² + 12xy
⇒ 64 = 4X² + 9y² + 12 x 2
⇒ 64 = 4x² + 9y² + 24
⇒ 4x² + 9y² = 64 – 24 = 40
∴ 4x² + 9y² = 40

Question 9.
If 3x -7y = 10 and xy = -1, find the value of 9x² + 49y²
Solution:
3x – 7y = 10, xy = -1
3x -7y= 10
Squaring both sides,
(3x – 7y)² = (10)²
⇒ (3x)² + (7y)² – 2 x 3x x 7y = 100
⇒  9X² + 49y² – 42xy = 100
⇒  9x² + 49y² – 42(-l) = 100
⇒ 9x² + 49y² + 42 = 100
∴ 9x² + 49y² = 100 – 42 = 58

Question 10.
Simplify each of the following products:

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.
Simplify each of the following products:

Solution:

Question 14.
Prove that a² + b² + c² – ab – bc – ca is always non-negative for all values of a, b and c.
Solution:

∵  The given expression is sum of these squares
∴ Its value is always positive Hence the given expression is always non-­negative for all values of a, b and c

Hope given RD Sharma Class 9 Solutions Chapter 4 Algebraic Identities Ex 4.1 are helpful to complete your math homework.

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RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS

Mark the correct alternative in each of the following:
Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.
The rationalisation factor of 2 + \(\sqrt { 3 } \)  is
(a) 2 – \(\sqrt { 3 } \)
(b) \(\sqrt { 2 } \) + 3
(c)  \(\sqrt { 2 } \) – 3
(d) \(\sqrt { 3 } \) – 2
Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

Question 15.

Solution:

Question 16.

Solution:

Question 17.

Solution:

Question 18.

Solution:

Question 19.

Solution:

Question 20.

Solution:

Question 21.

Solution:

Question 22.

Solution:

Question 23.

Solution:

Question 24.

Solution:

Question 25.

Solution:

Hope given RD Sharma Class 9 Solutions Chapter 3 Rationalisation MCQS are helpful to complete your math homework.

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RD Sharma Class 9 Solutions Chapter 3 Rationalisation VSAQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 3 Rationalisation VSAQS

Question 1.
Write the value of (2 + \(\sqrt { 3 } \) ) (2 – \(\sqrt { 3 } \)).
Solution:
(2+ \(\sqrt { 3 } \) )(2- \(\sqrt { 3 } \) ) = (2)²-(\(\sqrt { 3 } \) )²
{∵ (a + b) (a – b) = a² – b²}
= 4-3=1

Question 2.
Write the reciprocal of 5 + \(\sqrt { 2 } \).
Solution:

Question 3.
Write the rationalisation factor of 7 – 3\(\sqrt { 5 } \) .
Solution:
Rationalising factor of 7 – 3\(\sqrt { 5 } \) is 7 + 3\(\sqrt { 5 } \)
{∵ (\(\sqrt { a } \) + \(\sqrt { b } \)  ) (\(\sqrt { a } \) – \(\sqrt { b } \)) = a-b}

Question 4.

Solution:

Question 5.
If x =\(\sqrt { 2 } \) – 1 then write the value of \(\frac { 1 }{ x }\).
Solution:

Question 6.
If a = \(\sqrt { 2 } \) + h then find the value of a –\(\frac { 1 }{ a }\)
Solution:

Question 7.
If x = 2 + \(\sqrt { 3 } \), find the value of x + \(\frac { 1 }{ x }\).
Solution:

Question 8.
Write the rationalisation factor of \(\sqrt { 5 } \) – 2.
Solution:
Rationalisation factor of \(\sqrt { 5 } \) – 2 is \(\sqrt { 5 } \) + 2 as
(\(\sqrt { a } \) + \(\sqrt { b } \))(\(\sqrt { a } \) – \(\sqrt { b } \)) = a – b

Question 9.
Simplify : \(\sqrt { 3+2\sqrt { 2 } }\).
Solution:

Question 10.
Simplify : \(\sqrt { 3-2\sqrt { 2 } }\).
Solution:

Question 11.
If x = 3 + 2 \(\sqrt { 2 } \), then find the value of  \(\sqrt { x } \) – \(\frac { 1 }{ \sqrt { x } }\).
Solution:

Hope given RD Sharma Class 9 Solutions Chapter 3 Rationalisation VSAQS are helpful to complete your math homework.

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RD Sharma Class 9 Solutions Chapter 3 Rationalisation Ex 3.2

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 3 Rationalisation Ex 3.2

Question 1.
Rationalise the denominators of each of the following(i – vii):
>
Solution:

Question 2.
Find the value to three places of decimals of each of the following. It is given that

Solution:

Question 3.
Express each one of the following with rational denominator:

Solution:

Question 4.
Rationales the denominator and simplify:

Solution:

Question 5.
Simplify:

Solution:

Question 6.
In each of the following determine rational numbers a and b:

Solution:

Question 7.

Solution:

Question 8.
Find the values of each of the following correct to three places of decimals, it being given that \(\sqrt { 2 } \)  = 1.4142, \(\sqrt { 3 } \) = 1-732, \(\sqrt { 5 } \)  = 2.2360, \(\sqrt { 6 } \) =  2.4495 and \(\sqrt { 10 } \)  = 3.162.

Solution:

Question 9.
Simplify:

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 12.

Solution:

Hope given RD Sharma Class 9 Solutions Chapter 3 Rationalisation Ex 3.2 are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.