Determine if 3 is a root of the equation

Asked by admin @ 20/08/2021 in Math viewed by 347 People

Determine, if 3 is a root of the equation given below √x2-4x+3+√x2-9=√4x2-14x+16

Answered by admin @ 20/08/2021

Answer:

3 is not a root of given equation.

Step-by-step explanation:

$Given \: equation \\\sqrt{x^{2}-4x+3}+\sqrt{x^{2}-9}\\=\sqrt{4x^{2}-14x+16}$

Put x = 3 in the equation, we get

$\sqrt{3^{2}-4\times 3 +3}+\sqrt{3^{2}-9}\\=\sqrt{4\times 3^{2}-14\times 3+16}$

$\implies \sqrt{9-12+3}+\sqrt{9-9}\\=\sqrt{36-42+16}$

$\implies 0+0=\sqrt{52-42}$

$\implies 0= \sqrt{10}\:(False)$

Therefore,

3 is not a root of given equation.

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