Question 69

Divide 20 into two parts such that the sum of the square of the parts is 232. What is the value of the two parts?

Solution

Let the first part = $$x$$ and second part = $$(20 - x)$$

According to ques, => $$(x)^2 + (20 - x)^2 = 232$$

=> $$x^2 + (x^2 + 400 - 40x) = 232$$

=> $$2x^2 - 40x + 400 - 232 = 0$$

=> $$x^2 - 20x + 84 = 0$$

=> $$x^2 - 6x - 14x + 84 = 0$$

=> $$x(x-6) - 14(x-6) = 0$$

=> $$(x-6)(x-14) = 0$$

=> $$x = 6,14$$

=> Ans - (A)

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