Question 53

The difference between two numbers is 43 and their product is 50. Find the sum of their squares.

Solution

Let the two numbers are $$a$$ and $$b$$

Given, Product of numbers = 50

$$=$$> $$ab = 50$$

Difference of numbers = 43

$$=$$> $$a - b = 43$$

$$=$$> $$\left(a-b\right)^2=43^2$$

$$=$$> $$a^2+b^2-2ab=1849$$

$$=$$> $$a^2+b^2-2\left(50\right)=1849$$

$$=$$> $$a^2+b^2=1849+100$$

$$=$$> $$a^2+b^2=1949$$

$$ \therefore\ $$Sum of the squares of the numbers = 1949

Hence, the correct answer is Option B

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