Question

Plz answer......... ​

Answer 1

Explanation:

Let us consider a quadratic polynomial px^2+qx+r=0

we know that discriminant q^2-4pr=0

the roots of the equation are equal

Here, q=-2(a^2-bc) ;p=c^2-ab;r=b^2-ac

Therefore, discriminant =0

q^2=4pr

(-2(a^2-bc))^2 = 4( c^2-ab) ( b^2-ac)

4(a^4+b^2c^2-2a^2bc)=4(b^2c^2+a^2bc-ab^3)

a^4+b^2c^2-2a^2bc=b^2c^2+a^2bc-ab^3-ac^3

a^4+b^2c^2-2a^2bc-b^2c^2-a^2bc+ab^3+ac^3=0

a(a^3+b^3+c^3)=3a^2bc

a(a^3+b^3+c^3-3abc)=0

a=0or a^3+b^3+c^3-3abc=0

a=0or a^3+b^3+c^3=3abc

Hence, proved.

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Answer 2

Explanation:

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