Question

which of the following equation is not quadratic equation? (a) 2x-5/ x=3 (b) x-1/x=7 (c) 2x2-5x=x2+5 (d) x2+1/x=5​

Answer 1

Answer:

c will be the answer of the following question

Answer 2

$\bold{(a)2x - \frac{5}{x} = 3} \\ \\ \bold{: \implies \frac{2 {x}^{2} - 5}{x} = 3 } \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 2 {x}^{2} - 5 \: = 3x } \: \: \: \: \: \: \: \\ \\ \bold{: \implies 2 {x}^{2} - 3x - 5 = 0 }$

the equation is in the form of ax² + bx + c = 0

so, the equation is quadratic.

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$\bold{(b)x - \frac{1}{x} = 7 } \\ \\ \bold{: \implies \frac{ {x}^{2} - 1} {x} = 7} \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{2} - 1 = 7x } \: \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{2} - 7x - 1 = 0}$the equation in the form of ax² + bx + c = 0

so, the equation is quadratic

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$\bold{(c)2 {x}^{2} - 5x = {x}^{2} + 5} \\ \\ \bold{: \implies2 {x}^{2} - {x}^{2 } - 5 x - 5 = 0 } \\ \\ \bold{: \implies {x}^{2} - 5x - 5 = 0} \: \: \: \: \: \: \: \: \: \: \: \:$

the equation is in the form of ax² + bx + c = 0

so, the equation is quadratic

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$\bold{(d) {x}^{2} + \frac{1}{x} = 5 } \\ \\ \bold{: \implies \frac{ {x}^{3} + 1 }{x} = 5} \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies {x}^{3} + 1 = 5x} \: \: \: \: \: \: \: \\ \\ \bold{ : \implies {x}^{3} - 5x + 1 = 0 }$

the equation is in the form of ax³+ bx + c = 0

the equation is cubic

so, the equation is not quadratic

hence,(d) x2+1/x=5 is not quadratic equation