Question

Kindly do the question no. 11.

Answer 1

$given \: that \: 2x - 3y = 5 \\ and \: xy = 2 \\ {(2x - 3y)}^{2} = 4 {x}^{2} + 9 {y}^{2} - 2 \times \\ 2x \times 3y \\ {(5)}^{2} = 4 {x}^{2} + 9 {y}^{2} - 12xy \\ 25 = 4 {x}^{2} + 9 {y}^{2} - 12 \times 2 \\ 25 = 4 {x}^{2} + 9 {y}^{2} - 24 \\ 4 {x}^{2} + 9 {y}^{2} = 25 + 24 \\ 4 {x}^{2} + 9 {y}^{2} = 49 \: \: \: \: \: ans$

Answer 2

Question :-

If 2x - 3y = 5 and xy = 2 , find the value of 4${x}^{2}$ + 9 ${y}^{2}$

Answer :-

= 2x - 3y = 5

• Square on both sides

= ${(2x-3y)}^{2}$ = 25

= ${4x}^{2}$ - 2×2x×3y + ${9y}^{2}$ = 25

= ${4x}^{2}$ + ${9y}^{2}$ = 25 + 12(xy)

= ${4x}^{2}$ + ${9y}^{2}$ = 25 + 12(2)

= ${4x}^{2}$ + ${9y}^{2}$ = 25 + 24

= ${4x}^{2}$ + ${9y}^{2}$ = 49.

•°• 49 is your required answer.

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