Question

a2+1/a2=27 find a3-1/a3

Answer 1

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Answer 2

Answer:

Question: If  $(a^{2}+\frac{1}{a^2}) = 27,$  find the values of: i. $(a-\frac{1}{a} )$ ii. $(a^{3}-\frac{1}{a^3})$

Square the Question:

i.

• $(a-\frac{1}{a})^2 = a^2+\frac{1}{a^2}-2$
• $(a-\frac{1}{a})^2= 27-2$
• $(a-\frac{1}{a})^2 = 25$
• $a-\frac{1}{a} = \sqrt{25}$
• $a-\frac{1}{a} = 5$

Cube the Question

ii.

• $(a-\frac{1}{a})^3=5^3$
• $a^3-\frac{1}{a^3}-3(5)=125$
• $a^3-\frac{1}{a^3}-15=125$
• $a^3-\frac{1}{a^3}=125+15$
• $a^3-\frac{1}{a^3}=140$

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