Question

(x^2+5x-2)^2+x^2+5x-7=0
Quadratic equation
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Answer 1

Answer:

answer is x^4+x^2+25x^2+5x=11

Step-by-step explanation:

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Answer 2

Equation-

$\rm{ ({x}^{2} + 5x - 2)}^{2} + {x}^{2} + 5x - 7 = 0$

Here

$\rm \: let \: {x}^{2} + 5x \: be \: p$

Then

$\rm(p - 2 {)}^{2} + p - 7 = 0 \\ \rm \implies {p}^{2} + 4 - 4p - 7 = 0 \\ \rm \implies \boxed{ \rm{ p}^{2} - 4p - 3 = 0}$

Using quadratic formula

$\rm \: p = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \implies \rm p = \frac{4 \pm \sqrt{ {4}^{2} + 4 \times 1 \times 3 } }{ - 6} \\ \implies \rm \: p = \frac{4 \pm \sqrt{16 + 12} }{ - 6} \\ \rm \implies \: p = \frac{4 \pm2 \sqrt{6} }{ - 6} \\ \implies \rm \boxed{ p = - \frac{2 \pm \sqrt{6} }{3}}$

$\rm \boxed {{x}^{2} + 5x = - \frac {2 \pm \sqrt{6} }{3}}$

Finding discriminant of this question you will find that there roots are not real as d<0