Question

If m+1/m=underoot3, find m^3-1/m^3​

Answer 1

Answer:

$\huge{\boxed{\rm{\red{m³-1/m³=2i}}}}$

Step-by-step explanation:

Given that:

m+1/m=√3 ------(1)

squaring on both sides, then

(m+1/m)²=(√3)²

[(a+b)²=a²+2ab+b²]

=>m²+2(m)(1/m)+1/m²=3

=>m²+1/m²+2=3

=>m²+1/m²=3-2

=>m²+1/m²=1 ------(2)

We know that

(a-b)²=(a+b)²-4ab

(m-1/m)²=(m+1/m)²-4(m)(1/m)

=>(m-1/m)²=(√3)²-4

=>(m-1/m)²=3-4

=>(m-1/m)²=-1

=>m-1/m=√-1 =√i²=i-----(3)

now m³-1/m³=(m-1/m)(m²+1/m²+(m)(1/m))

[(a³-b³)=(a-b)(a²+ab+b²)]

=>m³-1/m³=(m-1/m)(m²+1/m²+1)

=>m³-1/m³=(i)(1+1)

=>m³-1/m³=2i

Used formulae:-

• (a+b)²=a²+2ab+b²
• (a-b)²=(a+b)²-4ab
• a³-b³=(a-b)(a²+ab+b²)
• -1=i²