Step-by-step explanation:
The answer is attached above
Answer:
3√3 - 3
m + 1/m = √3, m3 + 1/m3 = ?
We know that a3 + b3 = (a + b) (a2 + b2 - ab)
If we replace the values of a and b in the formula as per the question we get m3 + 1/m3 = (m + 1/m) {m2 + (1/m)^2 - m × 1/m)
= (√3) {m2 + 1^2 / m^2 - 1) (∵ (1/m)^2 = 1^2 / m^2)
= (√3) {m2 + 1/m2 - 1)
= (√3) {(m + 1/m)^2 - 2 × m × 1/m - 1) {∵ m2 + 1/m2 = (m + 1/m)^2 - 2 × m × 1/m}
= (√3) (√3)^2 - 2 - 1) (∵ replacing the value of m + 1/m with √3)
= √3 (√3)^2 - 3
= √3 × 3 - 3
= 3√3 - 3 (Ans)
Therefore, the value of m3 + 1/m3 is 3√3 - 3.
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Answers & Comments
Step-by-step explanation:
The answer is attached above
Answer:
3√3 - 3
Step-by-step explanation:
m + 1/m = √3, m3 + 1/m3 = ?
We know that a3 + b3 = (a + b) (a2 + b2 - ab)
If we replace the values of a and b in the formula as per the question we get m3 + 1/m3 = (m + 1/m) {m2 + (1/m)^2 - m × 1/m)
= (√3) {m2 + 1^2 / m^2 - 1) (∵ (1/m)^2 = 1^2 / m^2)
= (√3) {m2 + 1/m2 - 1)
= (√3) {(m + 1/m)^2 - 2 × m × 1/m - 1) {∵ m2 + 1/m2 = (m + 1/m)^2 - 2 × m × 1/m}
= (√3) (√3)^2 - 2 - 1) (∵ replacing the value of m + 1/m with √3)
= √3 (√3)^2 - 3
= √3 × 3 - 3
= 3√3 - 3 (Ans)
Therefore, the value of m3 + 1/m3 is 3√3 - 3.