Question 63

If $$a^{2}+b^{2}-c^{2}=0$$, then the value of $$\frac{2(a^{6}+b^{6}-c^{6})}{3a^{2}b^{2}c^{2}}$$ is:

Solution

If a + b + c = 0 then $$a^3 + b^3 + c^3 = 3abc$$ so,

$$a^{6}+b^{6}-c^{6} = 3a^2b^2c^2$$

$$\frac{2(a^{6}+b^{6}-c^{6})}{3a^{2}b^{2}c^{2}}$$

= $$\frac{2(3a^{2}b^{2}c^{2})}{3a^{2}b^{2}c^{2}}$$ = 2

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