Question

detrrmine if 3 is a root of the equation given below root over x square - 4 x + 3 + Root over x square minus 9 x is equal to root over 4 x square - 14 x + 16​

Answer 1

Step-by-step explanation:

3 is not a root of given equation.

Step-by-step explanation:

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

Givenequation

x

2

−4x+3

+

x

2

−9

=

4x

2

−14x+16

Put x = 3 in the equation, we get

\begin{lgathered}\sqrt{3^{2}-4\times 3 +3}+\sqrt{3^{2}-9}\\=\sqrt{4\times 3^{2}-14\times 3+16}\end{lgathered}

3

2

−4×3+3

+

3

2

−9

=

4×3

2

−14×3+16

\begin{lgathered}\implies \sqrt{9-12+3}+\sqrt{9-9}\\=\sqrt{36-42+16}\end{lgathered}

⟹

9−12+3

+

9−9

=

36−42+16

\implies 0+0=\sqrt{52-42}⟹0+0=

52−42

\implies 0= \sqrt{10}\:(False)⟹0=

10

(False)

Therefore,

3 is not a root of given equation.

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