Question

given , a+b=12 ,ab=32 then prove that , (a+2b)^2 - 5b^2 = 176
​

Answer 1

Step-by-step explanation:

${(a + 2b)}^{2} - 5 {b}^{2} = 176 \\ {a}^{2} + {(2b)}^{2} + 2 \times 2b \times a - 5 {b}^{2} = 176 \\ {a}^{2} + 4 {b}^{2} - 5 {b}^{2} + 4ab = 176 \\ {a}^{2} - {b}^{2} + 4 \times 32 = 176 \\ {a }^{2} - {b}^{2} = 176 - 128 \\ (a + b)(a - b) = 48 \\ (a - b) = \frac{48}{12} \\ (a - b) = 4$