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Question
`sqrt2x^2+7x+5sqrt2=0`
Solution
We write, `7x=5x+2x as sqrt2x^2xx5sqrt2=10x^2=5x xx 2x`
∴` sqrt2x^2+7x+5sqrt2=0`
⇒` sqrt2x^2+5x+2x+5sqrt2=0`
⇒` x(sqrt2x+5 )+sqrt2 (sqrt2x+5)=0`
⇒`(sqrt2x+5)(x+sqrt2)=0`
⇒`x+sqrt2=0 or sqrt2x+5=0`
⇒`x=-sqrt2 or x=-5/sqrt2=-(5sqrt2)/2`
Hence, the roots of the given equation are `-sqrt2` and `(-5sqrt2)/2`
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