Question

If the quadratic equation c square minus a b whole x square - 2 into a square x minus b c x + b square minus ac is equal to zero in x has equal roots ensure that either is equal to zero or a cube plus b cube plus c cube is equal to 3 abc

Answer 1

Answer:

(c^2-ab)*x^2-2(a^2-bc)x+(b^2-ac)=0

roots are equal in nature,

we know that,

b^2-4ac=0 -- >A)

the value of a is (c^2-ab)

the value of b is -2(a^2-bc)

the value of c is (b^2-ac)

put all these value in eq A)

[-2(a^2-bc)]²-4*[(c^2-ab)]*(b^2-ac)=0

4(a^2-bc)²-4[c²b²-ac³-ab³+a²bc]=0

4 can be cancelled out.

a^4-2bca^2+b^2c^2=b^2c^2-ac³-ab³+a²bc ---> x)  

1. a²bc can be cancelled out.

Now equation x can be written as

a^4-2a²bc+b²c²=b²c²-ac³-ab³+a²bc

a^4-3a²bc²+ac³+ab³=0

Taking a as common from equation,

a (a³-3abc²+c³+b³)=0

a³+b³+c³=3abc²

Answer 2

Answer :-

Here's your answer

Hope it helps