Question

${\red{\overline{\green{\underline{\orange{\boxed{\pink{\mathtt{Question}}}}}}}}}$

Say whether the following is a quadratic equations

(I)$\sf\pink{(x+1)^2=2(x-3)}$
(II)$\sf\red{(x-2)(x+1)=(x-1)(x+3)}$



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Answer 1

${\huge{\underbrace{\rm{Answer\checkmark}}}}$

★ Given -

• (x+1)² = 2(x-3)
• (x-2)(x+1) = (x-1)(x+3)

★ To Find -

• ${\tt{Which\; is \; a \; Quadratic\;equation}}$

★ Solution :

→ First Equation -

$\rm \: {(x + 1)}^{2} = 2(x - 3)$

$\mapsto \rm \: {x}^{2} + 1 + 2x = 2x - 6$

$\mapsto \rm \: {x}^{2} + 1 + { \cancel{2x}} - { \cancel{2x}} + 6 = 0$

$\mapsto \rm \: {x}^{2} + 7 = 0$

$\boxed{ \tt{ \star \: YES \: it \: is \: a \: quadratic \: eq}}$

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→ Second Equation -

$\rm \: (x - 2)(x + 1) = (x - 1)(x + 3)$

$\mapsto \rm \: {x}^{2} + x - 2x - 2 = {x}^{2} + 3x - x - 3$

$\mapsto \rm \: {x}^{2} - x - 2 = {x}^{2} + 2x - 3$

$\mapsto \rm \: \cancel{ {x}^{2}} - x - 2 - \cancel{ {x}^{2} } - 2x + 3 = 0$

$\mapsto \rm \: - 3x + 1 = 0$

$\boxed{ {\star \: }{ \tt{NO \: it \: is \: not \: a \: quadratic \: equation}}}$

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☑️ Quadratic Equations are in the form of :

$\boxed{ \rm{a {x}^{2} + bx + c}}$

In which ,

$\rm \: a ≠ 0$

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Answer 2

${\red{\overline{\green{\underline{\orange{\boxed{\pink{\mathtt{Answer}}}}}}}}}$

$\sf\blue{x+1)^2=2(x-3)}$

$\sf\blue{\pink\implies\frac{x}{2}+2x+1=2x-6}$

$\sf\blue{\red\implies\frac{x}{2}+7=0}$

$\sf\red{It\:is\:the\:form\:of\:the\form\:\frac{ax}{2}+bx+c=o.}$

Hence,the given equation is a quadratic equation .

$\sf\red{(x-2)(x+1)=(x-1)(x+3)}$

$\sf\blue{\pink\implies\frac{x}{2}-x-2=\frac{x}{2}+2x-3}$

$\sf\blue{\red\implies\:3x-1=0}$

$\sf\red{It\:is\not\:the\: \:form \:of\:the\form\:\frac{ax}{2}+bx+c=o.}$

Hence,the given equation is not a quadratic equation .