Question

Find the value of 4ab(a^2+b^2). if (a+b)=11 and (a-b)=1​

Answer 1

Step-by-step explanation:

$a + b = 11 \: \: \: \: \: \: \: \: a - b = 1 \\ \\ = 4ab( {a}^{2} + {b}^{2} ) \\ \\ = now \: use \: the \: equation \: of \: {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} \\ \\ put \: value \: in \: equation \\ \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ {1}^{2} = {a}^{2} + {b}^{2} - 2ab \: \: \: \: \: (a - b = 1) \\ \\ {a}^{2} + {b}^{2} = 1 + 2ab \\ \\ so \: \: {a}^{2} + {b}^{2} = 1 + 2ab \: ..............(1) \\ \\ = 4ab(1 + 2ab)...........from \: (1) \\ = 4ab + 8 {a}^{2} {b}^{2}$