If the sum of two numbers is 7 and sum of their cubes is 133, find the sum of their squares.
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If the sum of two numbers is 7 and sum of their cubes is 133, find the sum of their squares.

KnowledgeBoat · Accepted Answer

Let the two numbers be x and y. Given, Sum of two numbers is 7. ∴ x + y = 7 Sum of cubes of two numbers is 133. ∴ x3 + y3 = 133 By formula, ⇒ (x + y)3 = x3 + y3 + 3xy(x + y) Substituting values we get : ⇒ 73 = 133 + 3xy × 7 ⇒ 343 = 133 + 21xy ⇒ 21xy = 343 - 133 ⇒ 21xy = 210 ⇒ xy = = 10. By formula, ⇒ (x + y)2 = x2 + y2 + 2xy Substituting values we get : ⇒ 72 = x2 + y2 + 2 × 10 ⇒ 49 = x2 + y2 + 20 ⇒ x2 + y2 = 49 - 20 = 29. Hence, sum of the squares of the numbers = 29.

Mathematics

If the sum of two numbers is 7 and sum of their cubes is 133, find the sum of their squares.

Expansions

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Mathematics

If the sum of two numbers is 7 and sum of their cubes is 133, find the sum of their squares.

Expansions

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