Question

PLEASE HELP ME
it is very important question​

Answer 1

$3x - 4y = 10 \: and \: xy = - 1 \\ {(3x - 4y)}^{2} = {10}^{2} \\ 9 {x}^{2} + 16 {y}^{2} - 24xy = 100 \\ 9 {x}^{2} + 16 {y}^{2} = 100 - 24 \\ 9 {x}^{2} + 16 {y}^{2} = 76$

Answer 2

$\huge\color{cyan}\boxed{\colorbox{black}{ANSWER ❤}}$

If 3x - 4y = 10 and xy = -1 then the value of 9 x^{2}+16 y^{2} \text { is } 769x

2

+16y

2

is 76

Solution:

In the question it is given that

3x - 4y = 10 ……………(Equation 1)

xy = -1 …………….(Equation 2)

\text { We have to find the value of } 9 x^{2}+16 y^{2} We have to find the value of 9x

2

+16y

2

Squaring Equation 1 we get,

\begin{gathered}\begin{array}{l}{(3 x-4 y)^{2}=10^{2}} \\\\ {(3 x)^{2}+(4 y)^{2}-2.3 x .4 y=100} \\\\ {=9 x^{2}+16 y^{2}-24 x y=100}\end{array}\end{gathered}

(3x−4y)

2

=10

2

(3x)

2

+(4y)

2

−2.3x.4y=100

=9x

2

+16y

2

−24xy=100

Substituting the value of xy from equation 2, we get

\begin{gathered}\begin{array}{l}{=9 x^{2}+16 y^{2}-24(-1)=100} \\\\ {=9 x^{2}+16 y^{2}+24=100} \\\\ {9 x^{2}+16 y^{2}=100-24} \\\\ {9 x^{2}+16 y^{2}=76}\end{array}\end{gathered}

=9x

2

+16y

2

−24(−1)=100

=9x

2

+16y

2

+24=100

9x

2

+16y

2

=100−24

9x

2

+16y

2

=76

Thus the value of 9 x^{2}+16 y^{2}9x

2

+16y

2

is 76