If x3+4x=8 then x7+64x2=?
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x⁷ + 64x² = 128 if x³ + 4x = 8
Step-by-step explanation:
x³ + 4x = 8
x⁷ + 64x² = ?
x³ + 4x = 8
Squaring both sides
=> (x³ + 4x)² = 8²
=> x⁶ + 16x² + 8x⁴ = 64
Multiplying by x both sides
=> x⁷ + 16x³ + 8x⁵ = 64x
Adding 16x³ both sides
=> x⁷ + 32x³ + 8x⁵ = 64x + 16x³
=> x⁷ + 8x²(4x + x³) = 16(4x + x³)
using 4x + x³ = 8
=> x⁷ + 8x² * 8 = 16 * 8
=> x⁷ + 64x² = 128
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