Question

if a/b+b/a=1,then a3+b3=

Answer 1

Given a/b + b/a = 1

           (a^2 + b^2)/ab = 1.

           a^2 + b^2 = ab   --- (1)


Then a^3 + b^3 = (a + b)(a^2 + b^2 - ab)

                           = (a + b)(ab - ab)  (From (1))

                           = 0.


Hope this helps! :)

Answer 2

Answer:

The value of a³+b³ = 0

Step-by-step explanation:

Given

$\frac{a}{b}+\frac{b}{a} =1$

To find,

The value of a³+b³

Recall the formula

a³+b³ = (a+b)(a² -ab + b²)

Solution

Since $\frac{a}{b}+\frac{b}{a} =1$, we have

$\frac{a^2+b^2}{ab} = 1$

a² +b² = ab --------------(1)

a³+b³ = (a+b)(a² -ab + b²)

=(a+b)(ab -ab) (from equation(1)

= 0

∴a³+b³ = 0

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