Question

if X square + 1 by x square is equal to 7 find the value of x cube + 1 by x cube​

Answer 1

Answer:

x²+ 1/x² = 7

then we need to find x³ + 1/x³

SOLN:-

(x + 1/x)² = x²+ 1/x² + 2

(x + 1/x)² = 7 + 2

(x + 1/x)² = 9

∴ x + 1/x = ± 3

∴ (x + 1/x)³ = x³ + 1/x³ + 3x * 1/x(x + 1/x)

= (x + 1/x)³ = x³ + 1/x³ + 3(x + 1/x)

IF  x + 1/x = +3

then

= (x + 1/x)³ = x³ + 1/x³ + 3(x + 1/x)

= (3)³ = x³ + 1/x³ + 3²

= 27 - 9 =x³ + 1/x³

= x³ + 1/x³ = 18

IF  x + 1/x = -3

then

= (x + 1/x)³ = x³ + 1/x³ + 3(x + 1/x)

= (-3)³ = x³ + 1/x³ - 3²

= -27 + 9 =x³ + 1/x³

= x³ + 1/x³ = -18

∴ x³ + 1/x³ = ±18 ⇒ ANSWER

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