Question

If the difference between two positive nos. is 5 and the difference between their cubes is 650. Find their products and the sum of their squares. Please help !

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us assume that two given positive numbers are x & y .where x > y.

Than,

→ (x - y) = 5

Squaring both sides,

→ (x - y)² = 5²

→ x² + y² - 2xy = 25

→ x² + y² = (25 + 2xy) --------- Eqn(1) .

Also,

→ (x³ - y³) = 650

→ (x - y)(x² + y² + xy) = 650

→ 5(x² + y² + xy) = 650

→ (x² + y² + xy) = 130 ----------- Eqn(2).

Putting value of Eqn.(1) in Eqn.(2) Now,

→ 25 + 2xy + xy = 130

→ 3xy = 130 - 25

→ 3xy = 105

→ xy = 35 (Ans.)

Putting This value in Eqn.(1) Now,

→ x² + y² = 25 + 2*35

→ x² + y² = 25 + 70

→ x² + y² = 95 (Ans.)

Hence, products of given two positive numbers is 35 and the sum of their squares is 95.