If a + b = 7 and ab = 12, find the value of a2 + b2.

1.	If a + b = 7 and ab = 12, find the value of a2 + b2.
Answer» a + b = 7, ab = 12 Squaring, a + b = 7, both sides, (a + b)² = (7)² a² + b² + 2ab = 49 a² + b² + 2 x 12 = 49 a² + b² + 24 = 49 a² + b² = 49 - 24 a² + b² = 25

Answer»

a + b = 7, ab = 12

Squaring, a + b = 7, both sides,

(a + b)² = (7)²

a² + b² + 2ab = 49

a² + b² + 2 x 12 = 49

a² + b² + 24 = 49

a² + b² = 49 - 24

a² + b² = 25

Discussion

Simplify:(i) (x – y) (x + y) (x2 + y2) (x4 + y4)(ii) (2x – 1) (2x + 1) (4x2 + 1) (16x4 + 1)
Simplify:(m2 – n2m)2 + 2m3n2
Subtract the sum of 3l – 4m – 7n2 and 2l + 3m – 4n2 from the sum of 9l + 2m – 3n2 and -3l + m + 4n2….
Find the following products:(i) 2a3 (3a + 5b)(ii) -11a (3a + 2b)(iii) -5a (7a – 2b)(iv) -11y2 (3y + 7)
Evaluate each of the following when x = 2, y = -1. (3/5x2y) × (-15/4xy2) × (7/9x2y2)
Find the product of the following binomials:(i) (2x + y) (2x + y)(ii) (a + 2b) (a – 2b)(iii) (a2 + bc) (a2 – bc)
Find the following products: 4/3a (a2 + b2 – 3c2)
Find the product of the binomials: (x3 + 1/x3) (x3 – 1/x3)
If x + 1/x = 9 find the value of x4 + 1/ x4.
Find the product of the binomials:(x4 + 2/x2) (x4 – 2/x2)