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### Question

The sum of ages of two friends is 23, whereas the product of their ages is 126. What is the sum of squares of their ages?

**A**

277 years.

**B**

278 years.

**C**

276 years.

**D**

279 years.

**Soln.**

**Ans: a**

Let the ages be x and y. We are given x + y = 23, and xy = 126. Substituting in the identity $x^2 + y^2 = (x + y)^2 - 2 × xy$, we get $x^2 + y^2 = 23^2 - 2 × 126$ = 277.