Question

Can I please have help, I don't know how to solve this. 3741 = P(P-1) over 2

Answer 1

Answer:

The values of P are -87 or 86.

Step-by-step explanation:

Given:

$3741=\frac{P(P-1)}{2}$

Multiply by 2 on both the sides. This gives,

$3741\times 2=\frac{P(P-1)}{2}\times 2\\7482=P(P-1)$

Now, use distribution property.

$7482=P\times P - P\times 1\7482=P^2-P$

Now, add -7482 on both sides,

$P^2-P-7482=0$

This is a quadratic equation of the form $ax^2+bx+c=0$ which can be solved using quadratic formula with $a=1,b=-1,c=-7482$

$P=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\P=\frac{-1\pm\sqrt{(-1)^2-4(1)(-7482)}}{2(1)}\\P=\frac{-1\pm\sqrt{1+29928}}{2}\\P=\frac{-1\pm\sqrt{29929}}{2}\\P=\frac{-1-173}{2}\textrm{ or }P=\frac{-1+173}{2}\\P=\frac{-174}{2}\textrm{ or }P=\frac{172}{2}\\P=-87\textrm{ or }P=86$

Therefore, the values of P are -87 or 86