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Home » Find the roots of the following equations: (i) x-1/x = 3, x ≠ 0 (ii) 1/x+4 – 1/x-7 = 11/30, x = -4, 7
Find the roots of the following equations: (i) x-1/x = 3, x ≠ 0 (ii) 1/x+4 – 1/x-7 = 11/30, x = -4, 7
CBSE | Class 10 | Exercise 4.3 | Quadratic Equations
Find the roots of the following equations: (i) x-1/x = 3, x ≠ 0 (ii) 1/x+4 – 1/x-7 = 11/30, x = -4, 7

Solution:

\left( i \right)~x-1/x~=\text{ }3

\Rightarrow ~{{x}^{2}}~\text{ }3x~-1\text{ }=\text{ }0

On comparing the given equation with a{{x}^{2}}~+~bx~+~c~=\text{ }0 , we get

a~=\text{ }1,~b~=\text{ }-3\text{ }and~c~=\text{ }-1

By using quadratic formula, we get,

Ncert solutions class 10 chapter 4-5

\Rightarrow ~x~=~3\pm \surd 9+4/2

\Rightarrow ~x~=\text{ }3\pm \surd 13/2

\therefore ~x~=\text{ }3+\surd 13/2\text{ }or~x~=\text{ }3-\surd 13/2

 

\left( \mathbf{ii} \right)\text{ }\mathbf{1}/\mathbf{x}+\mathbf{4}\text{ }\text{ }\mathbf{1}/\mathbf{x}-\mathbf{7}\text{ }=\text{ }\mathbf{11}/\mathbf{30}
\Rightarrow ~x-7-x-4/\left( x+4 \right)\left( x-7 \right)\text{ }=\text{ }11/30

\Rightarrow -11/\left( x+4 \right)\left( x-7 \right)\text{ }=\text{ }11/30

\Rightarrow \left( x+4 \right)\left( x-7 \right)\text{ }=\text{ }-30

\Rightarrow ~{{x}^{2}}~\text{ }3x~\text{ }28\text{ }=\text{ }30

\Rightarrow ~{{x}^{2}}~\text{ }3x~+\text{ }2\text{ }=\text{ }0

We can solve this equation by factorization method now,

\Rightarrow ~{{x}^{2}}~\text{ }2x~~x~+\text{ }2\text{ }=\text{ }0

\Rightarrow ~x\left( x~\text{ }2 \right)\text{ }\text{ }1\left( x~\text{ }2 \right)\text{ }=\text{ }0

\Rightarrow \left( x~\text{ }2 \right)\left( x~\text{ }1 \right)\text{ }=\text{ }0

\Rightarrow ~x~=\text{ }1\text{ }or\text{ }2

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