Question

if a square +BE SQUARE =9AND AB =4 find the value of 3 (a+b)square -2 (a-b)square

Answer 1

a² + b² = 9

ab = 4

3(a+b)² - 2(a-b)²

⇒ 3(a²+ b² +2ab) - 2(a²+ b² - 2ab)

⇒ 3(9 + 8) - 2( 9-8)

⇒ 51 -2

⇒ 49

Answer 2

${a}^{2} + {b}^{2} = 9 \\ ab = 4 \\ {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ = 9 + 2 \times 4 = 9 + 8 = 17 \\ {( a-b )}^{2} = {a}^{2} + {b}^{2} - 2ab \\ = 9 - 2 \times 4 = 9 - 8 = 1 \\ 3 {( a+ b)}^{2} - 2 {(a -b )}^{2} \\ = 3 \times 17 - 2 \times 1 = 51 - 2 = 49$