Question
The difference between two positive numbers is $4$ and the difference between their cubes is $316.$Find : The sum of their squares
✓
Answer
Given difference between two positive numbers is $4$ and difference between their cubes is $316.$
Let the positive numbers be $a$ and $b$
$a - b = 4 .....(1)$
$a^3- b^3= 316 .....(2)$
$ab = 21 ......(3)$
Squaring $(1)$ both sides,
we get
$(a - b)^2= 16$
$a^2+ b^2- 2ab = 16$
$a^2+b^2=2 \times 21+16$
$a^2+b^2=42+16$
$a^2+b^2=58$
Sum of their squares is $58.$
Let the positive numbers be $a$ and $b$
$a - b = 4 .....(1)$
$a^3- b^3= 316 .....(2)$
$ab = 21 ......(3)$
Squaring $(1)$ both sides,
we get
$(a - b)^2= 16$
$a^2+ b^2- 2ab = 16$
$a^2+b^2=2 \times 21+16$
$a^2+b^2=42+16$
$a^2+b^2=58$
Sum of their squares is $58.$
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