Question

$(p^{2} + p - 5) \: (p^{2} + p - 4) = 6$
Answer properly wrong answer's will be reported ​

Answer 1

(p² + p - 5)(p² + p - 4) = 6

Let, P² + p = x

Hence, (x - 5)(x - 4) = 6

(x - 5) = 6 or (x - 4) = 6

x = 6 + 5 or x = 6 + 4

x = 11 or x = 10.

Now, when x = 11,

p² + p = 11

p² + p - 11 = 0

p = $\frac{ - 1± \sqrt{45} }{2}$

And, when x = 10,

p² + p = 10

p² + p - 10 = 0

p = $\frac{ - 1± \sqrt{41} }{2}$

Thus, The real roots i.e.,

p = $\frac{ - 1± \sqrt{45} }{2} or \frac{ - 1± \sqrt{41} }{2}$

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