## 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) (a^{2}b – b^{2}a)^{2}

(iv) (a – 0.1) (a + 0.1)

(v) (1.5.x^{2} – 0.3y^{2}) (1.5x^{2} + 0.3y^{2})

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 9x^{2} + 25y^{2} = 181 and xy = -6, find the value of 3x + 5y.

Solution:

9x^{2} + 25y^{2} = 181, and xy = -6

(3x + 5y)^{2} = (3x)^{2} + (5y)^{2} + 2 x 3x + 5y

⇒ 9X^{2} + 25y^{2} + 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 4X^{2} + 9y^{2}.

Solution:

2x + 3y = 8 and xy = 2

Now, (2x + 3y)^{2} = (2x)^{2} + (3y)^{2} + 2 x 2x x 3y

⇒ (8)^{2} = 4x^{2} + 9y^{2} + 12xy

⇒ 64 = 4X^{2} + 9y^{2} + 12 x 2

⇒ 64 = 4x^{2} + 9y^{2} + 24

⇒ 4x^{2} + 9y^{2} = 64 – 24 = 40

∴ 4x^{2} + 9y^{2} = 40

Question 9.

If 3x -7y = 10 and xy = -1, find the value of 9x^{2} + 49y^{2}

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

⇒ 9X^{2} + 49y^{2} – 42xy = 100

⇒ 9x^{2} + 49y^{2} – 42(-l) = 100

⇒ 9x^{2} + 49y^{2} + 42 = 100

∴ 9x^{2} + 49y^{2} = 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 a^{2} + b^{2} + c^{2} – 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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