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Question

If 5x-2y=7 and xy = 2 , then find the value of (5x+2y)^2


Solution

Given: 
5x-2y= 7
XY= 2

5x-2y = 7 

Squaring on both sides

(5x-2y)² = (7 )²

[( a-b)²= a²+b²-2ab]

(5x)² + (2y)² - 2× 5x× 2y = 49

(5x)² + (2y)² - 20xy= 49

(5x)² + (2y)² - 20 (2) = 49 [XY=20]


(5x)² + (2y)² - 40= 49

(5x)² + (2y)² = 49+ 40= 89

(5x)² + (2y)² = 89..............(1)

We have to find (5x+2y)²

(5x+2y)² = (5x)² + (2y)² + 2× 5x× 2y 

[( a+b)²= a²+b²+2ab]

(5x+2y)² = (5x)² + (2y)² + 2× 5x× 2y


(5x+2y)² = (5x)² + (2y)² + 20xy

Put the value of eq 1 


(5x+2y)² = 89 + 20 × 2

(5x+2y)² = 89+ 40 = 129

(5x+2y)² =129

Hence, the value of (5x+2y)² = 129

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