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### Question

The square root of twice my present age is equal to the sum of the square roots of my ages 7 years back and 7 years hence. What is my present age?

**A**

7 years.

**B**

8 years.

**C**

6 years.

**D**

14 years.

**Soln.**

**Ans: a**

Let the present age be x. Then $√(x - 7) + √(x + 7)$ = $√{2x}$. Squaring both sides, $(√(x - 7))^2 + (√(x + 7))^2 + 2√{x^2 - 7^2}$ = $2x$ which gives $x - 7 + x + 7 + 2√{x^2 - 7^2}$ = $2x$. Cancelling, and simplifying, $2√(x^2 - 49) = 0$, which leads to x = 7 years.