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Solve the following quadratic equation for x: x^2+(a/(a+b)+(a+b)/a)x+1=0 - CBSE Class 10 - Mathematics

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ConceptSolutions of Quadratic Equations by Factorization

Question

Solve the following quadratic equation for x:

x^2+(a/(a+b)+(a+b)/a)x+1=0

Solution

Given:

x^2+(a/(a+b)+(a+b)/a)x+1=0

Let a/(a+b)be t

Thus, the equation becomes

x^2+(t+1/t)x+1=0

x2+(t+1/t)x+1=0

x2+((t^2+1)/1)x+1=0

⇒tx2+(t2+1)x+t=0

tx2+t2x+x+t=0

(tx2+t2x)+(x+t)=0

tx(x+t)+1(x+t)=0

(tx+1)(x+t)=0

tx+1=0, x+t=0

=>x=(-1)/t,x= -t

=>x = (-1)/(a/(a+b)), x = -a/(a+b)

=>x= -(a+b)/a, x= -a/(a+b)

Is there an error in this question or solution?

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Solution Solve the following quadratic equation for x: x^2+(a/(a+b)+(a+b)/a)x+1=0 Concept: Solutions of Quadratic Equations by Factorization.
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