Question 91

Divide 32 into two parts such that the sum of the square of the parts is 674. What is the value of the parts?

Solution

Let the first part = $$x$$ and second part = $$(32 - x)$$

According to ques, => $$(x)^2 + (32 - x)^2 = 674$$

=> $$x^2 + (x^2 + 1024 - 64x) = 674$$

=> $$2x^2 - 64x + 1024 - 674 = 0$$

=> $$x^2 - 32x + 175 = 0$$

=> $$x^2 - 25x - 7x + 175 = 0$$

=> $$x(x-25) - 7(x-25) = 0$$

=> $$(x-25)(x-7) = 0$$

=> $$x = 25,7$$

=> Ans - (C)

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