Question

If a^2 + 1/a^2 = 14 find a^3 +1/a^3​

Answer 1

Step-by-step explanation:

a²+1/a²=14

(a+1/a)²-2•a•1/a= 14

(a+1/a)²-2=14

(a+1/a)²= 16

a+1/a= 4

on cubing both side

(a+1/a)³= 4³

a³+1/a³+3a•1/a(a+1/a)=64

a³+1/a³+3(a+1/a)=64

a³+1/a³+3×4=64

a³+1/a³+12=64

a³+1/a³= 52

#666

Answer 2

Given that :

${a}^{2} + \frac{1}{ {a}^{2} } = 14$

As we know that :

${a}^{2} + \frac{1}{ {a}^{2} } = {(a + \frac{1}{a}) }^{2} - 2a. \frac{1}{a} \\ \\ = > 14 = {(a + \frac{1}{a}) }^{2} - 2 \\ \\ = > {(a + \frac{1}{a}) }^{2} = 14 + 2 = 16 \\ \\ = > (a + \frac{1}{a}) = 4$

To find :

${a}^{3} + \frac{1}{ {a}^{3} } = {(a + \frac{1}{a} )}^{3} - 3(a. \frac{1}{a})(a + \frac{1}{a} ) \\ \\ = > {a}^{3} + \frac{1}{ {a}^{3} } = {(4)}^{3} - 3 \times 1 \times 4 \\ \\ = > {a}^{3} + \frac{1}{ {a}^{3} } = 64 - 12 = 52$

So, the correct answer will be 52 ✔✔

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Hope it helps ☺

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