Question

If 4x +7y = 28 and xy = 6, find the value of 16x2 + 49y2.​

Answer 1

448

Explanation:

4x +7y = 28 and xy = 6 (Given)

`{(4x + 7y)}^(2) = {(4x)}^(2) + {(7y)}^(2) + 2(4x)(7y) \\ \\ \implies \: {(4x + 7y)}^(2) = {16x}^(2) + {49y}^(2) + 56xy\\ \\ \implies \: {(28)}^(2) = {16x}^(2) + {49y}^(2) + 56(6) \\ \\ \implies \: 784 = {16x}^(2) + {49y}^(2) + 336 \\ \\ \implies \: {16x}^(2) + {49y}^(2) = 784 - 336\\ \\ \implies \: \huge \orange{ {16x}^(2) + {49y}^(2) =448}`