Question

Consider the equation y=sqrtx and y=x^2-1

The system of equation is equal at approximately?
1.5,1.2
-1.5,-1.2
1.5,-1.2
-1.5,1.2

Answer 1

the correct answer is 1.5,1.2
the x value should be positive because it's under the sqrt.
the y value is also positive from the first equation.

Answer 2

(1.5 , 1.2)

Explanation:

we are given system of equation as

`y=√(x)`

`y=x^2-1`

we can set them equal

and then we can solve for x

`y=x^2-1=√(x)`

we can take square both sides

`\left(x^2-1\right)^2=\left(√(x)\right)^2`

now, we can simplify it

`x^4-2x^2+1=x`

`x^4-2x^2-x+1=0`

now, we can draw graph and find x-intercept

so, x-intercepts are

(0.525,0)

(1.49,0)

now, we can find y-value

At x=1.49

`y=1.49^2-1`

`y=1.2`

So, point is (1.49 , 1.2)

or

(1.5 , 1.2)