Question

(9-10p)p=-40+(7-4p)(7+4p)​

Answer 1

Ответ:

p₁=$></p> <p>p₂=<img src=$

Пошаговое объяснение:

(9-10p)p=-40+(7-4p)(7+4p)

9p-10p²=-40+(49-16p²)

9p-10p²+40-49+16p²=0

6p²+9p-9=0

2p²+3p-3=0

D=b²-4ac=9-4*2*(-3)=9+24=33>0 ⇒2 корня.

p₁,₂=$\frac{-b\\\± \sqrt{D} }{2a}$

p₁=$></p> <p>p₂=<img src=$

Answer 2

Let's simplify the expression step by step:

Starting with the right-hand side:

(7-4p)(7+4p) = 49 - 16p^2 (using the FOIL method)

So now we have:

(9-10p)p = -40 + 49 - 16p^2

Simplifying further:

9p - 10p^2 = 9 - 16p^2

Moving all terms to one side:

0 = 25p^2 - 9p + 9

Now we can use the quadratic formula to solve for p:

p = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 25, b = -9, and c = 9. Plugging in these values:

p = (-(-9) ± sqrt((-9)^2 - 4(25)(9))) / 2(25)

p = (9 ± sqrt(441)) / 50

p = (9 ± 21) / 50

So the two possible solutions for p are:

p = 30/50 = 0.6

or

p = -12/50 = -0.24

Therefore, the two solutions to the original equation are p = 0.6 and p = -0.24.