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5(x + 1) + 5(2 - x) = 53 + 1, then find the positive value of x.
1. 2 or -1
2. 1
3. -1
4. 2 

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Correct Answer - Option 4 : 2 

Calculation:

5(x + 1) + 5(2 - x) = 53 + 1

⇒ 5x × 5 + 52 × 5-x = 125 + 1 = 126

⇒ 5y + 25/y = 126      ----(1) where, y = 5x

⇒ 5y2 - 126y + 25 = 0

⇒ 5y2 - 125y - y + 25 = 0

⇒ 5y(y - 5) - (y - 25) = 0

⇒ (5y - 1)(y - 25) = 0

⇒ y = 1/5 or y = 25

When, y = 1

⇒ 5x = 1/5 = 5-1

⇒ x = -1, which is not possible as we need only +ve value of x.

And, when y = 25

⇒ 5x = 25 = 52

x = 2 which is +ve

∴ The positive value of x is 2.

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