Question

if x+5y=9 and xy=4 tgen find x square 25y square

Answer 1

Given that : x+5y = 9

and xy = 4.....(1)

$x = \frac{4}{y}$

On putting the value of x in equation (1)

$\frac{4}{y} + 5y = 9 \\ \\ = > 4 + 5{y}^{2} = 9y \\ \\ = > 5{y}^{2} - 9y + 4 = 0 \\ \\ = > 5 {y}^{2} - 5y - 4y + 4 = 0 \\ \\ = > 5y(y - 1) - 4(y - 1) = 0 \\ \\ = > (y - 1)(5y - 4) = 0$

Required value of y = 1 and 4/5

when y = 1 then x = 4

when y = 4/5 then x = 5

Now,
${x}^{2} + 25 {y}^{2} \\ \\ = > {(5)}^{2} + 25 \times { (\frac{4}{5} )}^{2} \\ \\ = > 25 + 16 \\ \\ = > 41$