Question

if x2+1/x2 = 14, then the value of x3 + 1/x3 is​

Answer 1

Step-by-step explanation:

2x+1/2x=14

2x+1/x=14/2=7

3x=7-1=6

x=6/3=2

x=2

3×2+1/3×2

=6+1/3×2

=7/6

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Answer 2

Answer:

• 52

GivEn:-

• x²+1/x² = 14

To Find:-

• value of x³+1/x³

Step-by-step explanation:

$\implies \sf \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 14$

$\implies \sf \: {(x + \dfrac{1}{x} )}^{2} - 2 \times x \times \dfrac{1}{x} = 14$

$\implies \sf \: {(x + \dfrac{1}{x} )}^{2} = 14 + 2 = 16$

$\implies \sf \: {(x + \dfrac{1}{x} )}^{2} = {4}^{2}$

$\implies \sf \: {(x + \dfrac{1}{x} )} = {4}$

Now,

$\implies \sf \: {x}^{3} + \dfrac{1}{ {x}^{3} }$

$\implies \sf(x + \dfrac{1}{x} )^{3} - 3 \times x \times \dfrac{1}{x} (x + \dfrac{1}{x} )$

(putting the values..)

$\implies \sf \: {4}^{3} - 3 \times 4$

$\implies \sf \: 64 - 12$

$\implies \sf 52$