Question

if 5x-4y=8 and xy=12 . then find the value of :(5x+2y)^2​

Answer 1

Answer:

The value of expression ( 5 x + 2 y )² is 676

Step-by-step explanation:

Given as :

The linear expression as

5 x - 4 y = 8             ......1

And

x y = 12                   ........2

or, x = $\dfrac{12}{y}$

Put the value of y in eq 1

i.e 5 x - 4 y = 8

Or, 5 × $\dfrac{12}{y}$ - 4 y = 8

Or, $\dfrac{60}{y}$ - 4 y = 8

Or, 60 - 4 y² = 8 y

Or, y² + 2 y - 15 = 0

or, y² + 5 y - 3 y - 15 = 0

Or, y ( y + 5) - 3 ( y + 5 ) = 0

i.e ( y + 5 ) ( y - 3 ) = 0

∴   y = 3 , -5

Or, y = 3

Put the value of y into eq 2

x = $\dfrac{12}{y}$

Or, x = $\dfrac{12}{3}$

∴   x = 4

Again

The expression is ( 5 x + 2 y )²

Putting the value of x , y

i.e ( 5 × 4 + 2 × 3 )²

= ( 20 + 6 )²

= 26 ² = 676

Hence, The value of expression ( 5 x + 2 y )² is 676 Answer