Question

(3x+1)³+(x-3)³+(4-2x)³-6(3x+1)(x-3)(x-2)=0 than find the value x​

Answer 1

this is the write answer

Answer 2

value of x = -1

Before going to solve, let's know some important formula regarding the same.

if a + b + c = 0 then a³ + b³ + c³ - 3abc = 0

here given, (3x + 1)³ + (x - 3)³ + (4 - 2x) + 6(3x + 1)(x - 3)(x - 2) = 0

⇒(3x + 1)³ + (x - 3)³ + {-2(x - 2)}³ -3(3x + 1)(x - 3){-2(x - 2)} = 0

we see it follows a³ + b³ + c³ - 3abc = 0

then must be a + b + c = 0

⇒(3x + 1) + (x - 3) + {-2(x - 2)} = 0

⇒3x + 1 + x - 3 + 4 - 2x = 0

⇒2x + 2 = 0

⇒x = -1

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