Question

If (5x-2y) = 5 and xy=1, find the value of (5x+2y)^2

Answer 1

Answer:

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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Step-by-step explanation:

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Answer 2

Question :

If (5x-2y) = 5 and xy=1, find the value of (5x+2y)²

Given Data :

→ (5x – 2y) = 5

→ xy = 1 ____ (1)

To find :

the value of (5x+2y)²

Solution :

(5x – 2y)² = 25x² + 4y² – 2xy

So we know the value of 5x - 2y and xy

(5)² = 25x² + 4y² – 2 × 1

25x² + 4y² = 25 + 2

25x² + 4y² = 27 ____ (2)

So, now we need to use the formula (a + b)² = a² + b² + 2ab

(5x+2y)² = 25x² + 4y² + 2xy

As we know the values of 25x² + 4y² and 2xy from (2) and (1)

(5x+2y)² = 27 + 2

(5x + 2y)² = 29

$\sf \small5x + 2y = \pm \sqrt{29}$

• So the answer is ±√29