Question

if x+y=5 x²+y²=13 find value of x³+y³
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Answer 1

Answer:

35

Step-by-step explanation:

x + y = 5

Squaring both sides,

(x + y)² = 25

x² + y² + 2xy = 25

13 + 2xy = 25__________________________________(∵ x² + y² = 13)

2xy = 12

xy = 6

x³ + y³ = (x + y)(x² - xy + y²) = 5*(13-6) = 5 * 7 = 35

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Answer 2

Answer

35 is the value of x³+y³

Explanation

Given that: ( x + y ) = 5

Squaring both sides:

⟹ ( x + y )² = (5)²

⟹ ( x + y )² = 25

by using identity: ( x + y)² = x² + 2xy + y²

⟹ x² + 2xy + y² = 25

⟹ (x² + y²) + 2xy = 25

Given value of ( x² + y² ) is 13, By substituting the value of ( x² + y² ) as 13

⟹ 13 + 2xy = 25

⟹ 2xy = 25 - 13

⟹ 2xy = 12

⟹ xy = 12/2

⟹ xy = 6

We get xy as 6

We need to find x³ + y³

By using identity: x³ + y³ = (x + y)( x² + y²- xy )

⟹ (x + y)( x² + y²- xy )

Substituting 5 in place of (x + y)

⟹ 5( x² + y²- xy )

Substituting 13 in place of x²+y²

⟹ 5[( 13 ) - xy )]

Substituting 6 in place of xy

⟹ 5( 13 - 6 )

⟹ 5( 7 )

⟹ 35

35 is the value of x³+y³