R.D. Sharma Solutions Class 9th: Ch 4 Algebraic Identities Exercise 4.1

Chapter 4 Algebraic Identities R.D. Sharma Solutions for Class 9th Math Exercise 4.1

Exercise 4.1

1. Evaluate each of the following using identities :
(i) (2x-1/x)²(ii) (2x + y) (2x − y)
(iii) (a²b - b²a)²
(iv) (a - 0.1) (a + 0.1)
(v) (1.5x²− 0.3y²) (1.5x²+ 0.3y²)

Solution

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

Solution

3. Simplify each of the following :
(i) 175 × 175 + 2 × 175 × 25 + 25 × 25
(ii) 322 × 322 − 2 × 322 × 22 + 22 × 22
(iii) 0.76 × 0.76 + 2 × 0.76 × 0.24 + 0.24 × × 0.24

(iv) (7.83 ×7.83−1.17×1.17)/6.6

Solution

4. If

x + \frac{1}{x} = 11,

find the value of

x^{2} + \frac{1}{x^{2}}

Solution

5. If

x - \frac{1}{x} = - 1

, find the value of

x^{2} + \frac{1}{x^{2}}

Solution

6. If

x + \frac{1}{x} = \sqrt{5}

,find the value of

x^{2} + \frac{1}{x^{2}}

.

Solution

7. If

x^{2} + \frac{1}{x^{2}} = 66

find the value of

x - \frac{1}{x}

Solution

8. If

x^{2} + \frac{1}{x^{2}} = 79

, find the value of

x + \frac{1}{x}

Solution

9. If 9x²+ 25y² = 181 and xy = −6, find the value of 3x + 5y.

Solution

10. If 2x + 3y = 8 and xy = 2, find the value of 4x² + 9y²

Solution

11. If 3x − 7y = 10 and xy = -1, find the value of 9x² + 49y²

Solution

12. Simplify each of the following products:

Solution

13. Prove that a² + b² + c² −ab−bc−ca is always non-negative for all values of a, b, and c.

Solution

Squares of the numbers are always positive, therefore the number is always positive.