Question

If 2x - 5y = 8 and xy = 4, find the value of 4x2 + 25y2.​

Answer 1

Step-by-step explanation:

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Answer 2

The value of 4x² + 25y² = 144

Given :

2x - 5y = 8 and xy = 4

To find :

The value of 4x² + 25y²

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that 2x - 5y = 8 and xy = 4

Step 2 of 2 :

Find value of 4x² + 25y²

We use the formula

(a - b)² = a² - 2ab + b²

Thus we get

$\sf {(2x - 5y)}^{2} = {(2x)}^{2} - 2.2x.5y + {(5y)}^{2}$

$\displaystyle \sf{ \implies } {(2x - 5y)}^{2} = 4{x}^{2} - 20xy + 25{y}^{2}$

$\displaystyle \sf{ \implies } {(2x - 5y)}^{2} = 4{x}^{2} + 25{y}^{2} - 20xy$

$\displaystyle \sf{ \implies } {(8)}^{2} = 4{x}^{2} + 25{y}^{2} -( 20 \times 4)$

$\displaystyle \sf{ \implies } 64 = 4{x}^{2} + 25{y}^{2} - 80$

$\displaystyle \sf{ \implies } 4{x}^{2} + 25{y}^{2} = 80 + 64$

$\displaystyle \sf{ \implies } 4{x}^{2} + 25{y}^{2} = 144$

The value of 4x² + 25y² = 144

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