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Question

Solve the given quadratic equation by factorisation method, (2x3)=2x22x+21

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Solution

The given equation (2x3)=2x22x+21 can be simplified as follows:
(2x3)=2x22x+21(2x3)2=(2x22x+21)2(2x)2+32(2×2x×3)=2x22x+21((ab)2=a2+b22ab)4x2+912x=2x22x+214x2+912x2x2+2x21=02x210x12=02(x25x6)=0x25x6=0

Now, the quadratic equation x25x6=0 can be factorised as shown below:

x25x6=0x26x+x6=0x(x6)+1(x6)=0(x+1)=0,(x6)=0x=1,x=6

Hence, x=1 or x=6.

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