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प्रश्न
The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares
उत्तर
Given difference between two positive numbers is 4 and difference between their cubes is 316.
Let the positive numbers be a and b
a - b = 4 .....(1)
a3 - b3 = 316 .....(2)
ab = 21 .....(3)
Squaring(eq 1) both sides, we get
(a - b)2 = 16
a2 + b2 - 2ab = 16
a2 + b2 = 2 × 21 + 16
a2 + b2 = 42 + 16
a2 + b2 = 58
Sum of their squares is 58.
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