1.

If it is given that x2 – 2x = 34, find the value of (x + 5)2 + 1/(x + 5)2?1. 1192. 1423. 1674. 98

Answer» Correct Answer - Option 2 : 142

Given:

x2 – 2x = 34

Formula used:

(x + y)2 = x2 + y2 + 2ab

Calculation:

∵ x2 – 2x = 34

Adding and subtracting 5x on LHS;

⇒ x2 + 5x – 5x – 2x = 34

⇒ x2 + 5x – 7x = 34

Subtracting 35 on both sides;

⇒ x2 + 5x – 7x – 35 = 34 – 35

⇒ x(x + 5) – 7(x + 5) = (-1)

⇒ (x + 5)(x – 7) = (-1)

⇒ x – 7 = (-1)/(x + 5)

⇒ x + 1/(x + 5) = 7

Adding 5 both sides;

⇒ (x + 5) + 1/(x + 5) = 12

Squaring both sides;

⇒ (x + 5)2 + 1/(x + 5)2 + 2 = 144

⇒ (x + 5)2 + 1/(x + 5)2 = 144 – 2 = 142


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