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(x-3)³+5=x³+7x²-1plz answer​

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Correct Question:

Prove the below equation as quadratic:

(x - 3)³+ 5 = x³ + 7x² - 1

Solution:

Given equation:

(x - 3)³ + 5=x³ + 7x²- 1

Identity to be used to split it:

(x - y)³ = x³ - y³ - 3x²y + 3xy²

Spilt the term using this identity:

(x - 3)³ = x³ - 27 - 3(x²)(3) + 3(x)(9)

= x³ - 27 - 9x² + 27x

Put this value in the equation:

(x - 3)³ + 5 = x³ + 7x² - 1

=> x³ - 27 - 9x² + 27x + 5 = x³ + 7x² - 1

Take every term to LHS [Note that the SIGNS change while transposing]:

=> x³ - 27 - 9x² + 27x + 5 - x³ - 7x² + 1 = 0

=> -16x² + 27x - 21 = 0

=> -(16x² - 27x + 21) = 0

=> 16x² - 27x + 21 = 0

Note that a quadratic equation is an equation with DEGREE 2.

Since this simplified equation has a degree 2, it is a quadratic equation.


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