Question

(x^2+9x+61)^2=(x^2+3x-25)^2

Answer 1

(x^2+9x+61)^2=(x^2+3x-25)^2

|x^2+9x+61|=|x^2+3x-25|

x^2+9x+61=x^2+3x-25

x^2+9x+61 - x^2- 3x +25=0

6x+86=0

x= - 86/6= - 43/3

Answer 2

To solve the equation $(x^2 + 9x + 61)^2 = (x^2 + 3x - 25)^2$, we can follow these steps:

Step 1: Expand both sides of the equation. $(x^2 + 9x + 61)^2 = (x^2 + 3x - 25)^2$ $x^4 + 18x^3 + 189x^2 + 1107x + 3721 = x^4 + 6x^3 + 9x^2 + 6x - 25x^2 - 150x + 625$

Step 2: Simplify the equation by combining like terms. $x^4 + 18x^3 + 189x^2 + 1107x + 3721 = x^4 + 6x^3 - 16x^2 - 144x + 625$

Step 3: Rearrange the equation, bringing all terms to one side. $x^4 + 18x^3 + 189x^2 + 1107x + 3721 - (x^4 + 6x^3 - 16x^2 - 144x + 625) = 0$

Step 4: Combine like terms again. $x^4 + 18x^3 + 189x^2 + 1107x + 3721 - x^4 - 6x^3 + 16x^2 + 144x - 625 = 0$

Simplifying further: $12x^3 + 173x^2 + 963x + 2096 = 0$

At this point, we have a cubic equation. To find its roots, we can use numerical methods, such as graphing, factoring, or using numerical approximation techniques like Newton's method.

However, note that it's possible there may be no real solutions to this equation. If you're looking for real solutions, it would be best to use a numerical method or a computer algebra system to find the approximate solutions.