Question

Solve the equation (\sqrt{x^{2}-3x})=2x-6, inequality, or system of equations.

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asked 2021-06-10
Solve the equation \((\sqrt{x^{2}-3x})=2x-6\), inequality, or system of equations.

Answers (1)

2021-06-11

Step 1
To solve the equation: \((\sqrt{x^{2}-3x})=2x-6\)
Solution:
\((\sqrt{x^{2}-3x})=2x-6\)
on squaring both sides we get:
\(\Rightarrow (\sqrt{x^{2}-3x})^{2}=(2x-6)^{2}\)
\(\Rightarrow x^{2}-3x=(2x)^{2}-2(2x)(6)+6^{2}\)
\(\Rightarrow x^{2}-3x=4x^{2}-24x+36\)
\(\Rightarrow x^{2}-4x^{2}-3x+24x-36=0\)
\(\Rightarrow -3x^{2}+21x-36=0\)
\(\Rightarrow -3x^{2}+12x+9x-36=0\)
\(\Rightarrow -3x(x-4)+9(x-4)=0\)
\(\Rightarrow (x-4)(-3x+9)=0\)
\(\Rightarrow (x-4)=0, or (-3x+9)=0\)
\(\Rightarrow x=4, or 3x=9. \Rightarrow x=3\)
Step 2
Result:
Required solutions are, \(x=\{3,4\}\)

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