Question

If the sum of two number is 20 and
their cube is 2240. Find the sum of their
square
A. 206
B. 208
C. 210
D. 212​

Answer 1

Answer:

Let the two numbers be x and y.

According to the given condition

》x + y = 20 ... (1)

》x³ + y³ = 2240 ... (2)

a³ + b³ = (a + b)³ - 3ab (a + b)

We get

》2240 = 8000 - 3 ab (20)

》60 ab = 5760

》ab = 96

Now,

》x³ + y³ = (x + y) (x² + y² - xy)

》2240 = 20 (x² + y² - 96)

》x² + y² - 96 = 112

》x² + y² = 208