Question

check whether the following are quadratic equations or not X + 1 whole square equals to 2 into x minus 3 whole square​

Answer 1

Answer

Yes, (x + 1)² = 2(x - 3)² is a quadratic equation

$\rule{200}2$

Given

(x + 1)² = 2(x - 3)²

To check whether it is a quadratic equation or not

Solution  

First of all, solve both LHS and RHS

(x + 1)² = 2(x - 3)²

⇒ x² + 1 + 2x = 2(x² + 9 - 6x)

⇒ x² + 1 + 2x = 2x² + 18 - 12x

Now transposing all terms on RHS

⇒ 2x² - 12x + 18 - x² - 1 - 2x = 0

⇒ x² - 14x + 17 = 0

Since, the final equation is x² - 14x + 17 = 0 the equation is quadratic (because the degree of polynomial is 2).

Answer 2

QUESTION :-

check whether the following are quadratic equations or not X + 1 whole square equals to 2 into x minus 3 whole square.

SOLUTION :-

➠ (x +1)² = 2(x -3)²

➠ $\red{[(a+b)^2 = a^2 + b^2 +2ab]}$

➠ x² + 1 + 2x = 2 ( x²+9-6x)

➠ x² +1+2x = 2x²+18-12x

➠ 2x² -12x +18-x²-1-2x = 0

➠ x² - 14x +17=0

➠since, it is of the form ax²+bx+c = 0.

➠ [ where, a = 1 , b = 14 , c = 17 ]

➠ .°. it is a quadratic equation.