(x-3)³+5=x³+7x²-1
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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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