Question

If 5x – 4y =8 and xy=12, then find the value of (5x+4y)^2



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Answer 1

$\textsf{Given:}$

$\textsf{5x-4y=8 and xy=12}$

$\textsf{We know that}$

$\boxed{\mathsf{(a+b)^2=(a-b)^2+4ab}}$

$\implies\mathsf{(5x+4y)^2=(5x-4y)^2+4(5x)(4y)}$

$\implies\mathsf{(5x+4y)^2=(5x-4y)^2+80xy}$

$\implies\mathsf{(5x+4y)^2=8^2+80(12)}$

$\implies\mathsf{(5x+4y)^2=64+960}$

$\therefore\boxed{\mathsf{(5x+4y)^2=1024}}$

Answer 2

The value of  $(5x+4y)^2$ is 1024.

Step-by-step explanation:

We have,

5x - 4y =8 ......(1)

and

xy=12 .....(2)

Equation(2) can be written as : $y=\dfrac{12}{x}$ .....(3)

Equation (1) becomes:

$5x - 4(\dfrac{12}{x})=8\\\\5x-\dfrac{48}{x}=8\\\\5x^2-48=8x\\\\5x^2-8x-48=0$

On solving the above quadratic equation we get :

x = 4 or -2.4

Put x = 4 and x = -2.4 in equation (3).

y = 3 or y = -5

We need to find the value of $(5x+4y)^2$.

Case 1,

If x = 4 and y = 3

$=(5x+4y)^2\\\\=(5(4)+4(3))^2\\\\=1024$

Case 2,

If x = -2.4 and y = -5

$=(5x+4y)^2\\\\=(5(-2.4)+4(-5))^2\\\\=1024$

So, the value of  $(5x+4y)^2$ is 1024.

Learn more,

Solution of two equation

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