If x + y = 8 and x2 + y2 = 40, find the value of x3 + y3.
Answers
Answered by
2
Given,
x + y = 8
x² + y² = 40
so,
(x + y)² = (x² + y²) + 2xy
8² = 40 + 2xy
24 = 2xy
12 = xy
now,
x³ + y³ = (x + y)³ -3xy(x + y)
= (8)³ - 3×12 × 8
= 512 - 288
= 224
x + y = 8
x² + y² = 40
so,
(x + y)² = (x² + y²) + 2xy
8² = 40 + 2xy
24 = 2xy
12 = xy
now,
x³ + y³ = (x + y)³ -3xy(x + y)
= (8)³ - 3×12 × 8
= 512 - 288
= 224
Answered by
1
x+y = 8
x²+y² = 40
⭐x³ + y³ = (x+y)³ - 3xy(x + y)⭐
we need to find, value of xy
(x+y)² = x²+y² + 2xy
8² = 40 + 2xy
64 - 40 = 2xy
xy = 24/2
xy = 12
x³ + y³ = (8)³ - 3(12)(8)
= 512 - 288
= 224
hope it helps
x²+y² = 40
⭐x³ + y³ = (x+y)³ - 3xy(x + y)⭐
we need to find, value of xy
(x+y)² = x²+y² + 2xy
8² = 40 + 2xy
64 - 40 = 2xy
xy = 24/2
xy = 12
x³ + y³ = (8)³ - 3(12)(8)
= 512 - 288
= 224
hope it helps
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