This is relationship is an inverse variation. In this relationship the product of x and y always equals a constant. In this case the product is 8. i.e. xy = 8.
If the triangle is a right triangle, then
(3x)² + x² = (10)² .
9x² + x² = 100
10x² = 100
x² = 10
x = √10 = approx. 3.1622...
If ' x ' is <em>anything less than √10</em> , then the short sides are too short
to make a right angle at the top, and the angle where they meet
is obtuse.
' x ' has to be greater than 2.5 ... otherwise the two short sides
can't stretch far enough to reach both ends of the long side (10) .
So, if 2.5 < x < √10 , then there is a triangle, and it's obtuse.
Hi there!
To solve this equation, we can use distributive property.
I listed the terms you have to multiply :
x² × x² = x^4
x² × 2x = 2x³
x² × 5 = 5x²
2x × x² = 2x³
2x × 2x = 4x²
2x × 5 = 10x
-1 × x² = -x²
-1 × 2x = -2x
-1 × 5 = -5
Add all of them....
x^4 + 2x³ + 5x² +2x³ + 4x² + 10x - x² - 2x - 5
add up the like terms to simplify
x^4 + 4x³ + 8x² + 8x - 5
Hope this helped! :)
F(x)=(x-10)(x+6) and set it equal to 0 you will get x-10=0 and x+6=0 so x=10 and x=-6
