P^2-4p=1 step by step explanation pleaseee

Question

asked Mar 21, 2021 122k views

1 Answer

Muayad Salah · Answer 1 · 2021-03-26T02:39:09+0000

Answer:

$p_1=2+ √(5)\\p_2=2- √(5)$

Explanation:

A second-degree equation is often expressed as:

ax^2+bx+c=0

where a,b, and c are constants.

Solving with the quadratic formula:

$\displaystyle x=(-b\pm √(b^2-4ac))/(2a)$

The equation to solve is:

p^2-4p=1

We need to express the equation as mentioned above. The right side of the equation must be zero, so we subtract 1:

p^2-4p-1=0

Now we have the values to solve the equation:

a=1, b=-4, c=-1

Applying the formula:

$\displaystyle p=(-(-4)\pm √((-4)^2-4(1)(-1)))/(2(1))$

$\displaystyle p=(4\pm √(16+4))/(2)$

$\displaystyle p=(4\pm √(20))/(2)$

Since 20=4*5:

$\displaystyle p=(4\pm √(4*5))/(2)$

Taking the square root of 4:

$\displaystyle p=(4\pm 2√(5))/(2)$

Simplifying by 2:

$p=2\pm √(5)$

Two solutions are found:

$\boxed{p_1=2+ √(5)}\\\boxed{p_2=2- √(5)}$