Question

X
${x}^{4} + \frac{1}{ {x}^{4} } = 47 \: then \: find \: {x}^{3} + \frac{1}{ {x}^{3} }$
​

Answer 1

Step-by-step explanation:

x⁴+1/x⁴= 47

(x²)²+(1/x²)²+2 = 49

we know that.

a²+b²+2ab = (a+b)²

(x²+1/x²)² = 49

x²+1/x² = √49 = 7

(x)²+(1/x)²+2 = 9

(x+1/x)² = 9

(x+1/x) = √9 = 3

(x+1/x)³ = x³+1/x³+3(x)(1/x) [ x+1/x ]

(3)³ = x³+1/x³+3(3)

27 = x³+1/x³+9

27-9 = 18 => x³+1/x³

hope this helps