Question

Help w/ Quadratic Equations 3?

Hi please solve the following FIND X, show your work and be visual if you can!

Answer 1

The solutions are `S={2.62,0.38}`

Explanation:

We apply Pythagoras' theorem to `DeltaQSR`

`QR^2=QS^2+SR^2=(2x-1)^2+(3x-1)^2`

Then, to `DeltaQSP`

`PQ^2=PS^2+SQ^2=x^2+(2x-1)^2`

Then, to `DeltaQPR`

`PR^2=PQ^2+QR^2`

`(x+3x-1)^2=x^2+(2x-1)^2+(2x-1)^2+(3x-1)^2`

`16x^2-8x+1=x^2+4x^2-4x+1+4x^2-4x+1+9x^2-6x+1`

`16x^2-8x+1=18x^2-14x+3`

`2x^2-6x+2=0`

`x^2-3x+1=0`

`x=(3+-sqrt(9-4))/2=(3+-sqrt5)/2`

So,

`x_1=(3+sqrt5)/2=2.62`

`x_2=(3-sqrt5)/2=0.38`