solve
this problem
x² + 1/4x² = 8 find x³ + 1/8x³
Answers
Answer:
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Answer:
22 ½ is the answer
Step-by-step explanation:
x² + 1/4x² = 8 find x³ + 1/8x³
=> x² + 1/4x² = 8
=> (x)² + (1/2x)² + 1 = 8
=> (x + 1/2x)² = 8+1
=> (x + 1/2x)² = 9
=> x + 1/2x = 3
Cubing both side
=> (x + 1/2x)³ = (3)³
=> x³ + 3(x)²(1/2x) + 3(x)(1/2x)² + 1/8x³ = 27
=> x³ + 3(x)(1/2x)[x + 1/2x]+ 1/8x³ = 27
=> x³ + 3/2(x + 1/2x) + 1/8x³ = 27
=> x³ + 1/8x³ = 27 - 3/2(3)
=> x³ + 1/8x³ = 27 - 9/2
=> x³ + 1/8x³ = 54 - 9/2
=> x³ + 1/8x³ = 45/2
=> x³ + 1/8x³ = 22½ (Ans)