Question

4. If 5x – 2y = 7 and xy = 2, find the value of (5x + 2y)?​

Answer 1

Given:-

• 5x - 2y = 7
• xy = 2

⠀

To find:-

• Value of (5x + 2y)².

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Solution:-

→ (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

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• Put the value of eq 1.

→ (5x+2y)² = 89 + 20 × 2

→ (5x+2y)² = 89+ 40 = 129

→ (5x+2y)² = 129

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Hence,

• the value of (5x + 2y)² is 129.

Answer 2

Answer:

$\huge{\bf{\underline{\red{Solution:- :}}}}$

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 = $\boxed{\pink{89}}$

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

$\huge{\bf{\underline{\red{Answer :}}}}$

Hence, the value of (5x+2y)² = 129