Exercise 22 Page 261

We will find and check the solutions of the given equation.

Finding the Solutions

To solve equations with a variable expression inside a radical, we first want to make sure the radical is isolated. Then we can raise both sides of the equation to a power equal to the index of the radical. Let's try to solve our equation using this method! We now have a quadratic equation, and we need to find its roots. To do it, let's identify the values of a, b, and c. Since in our case a is the variable, let's use letters d, e and f instead. a^2 -4a +7 = 0 ⇕ 1a^2+( - 4)a+ 7=0 We can see that d= 1, e= - 4, and f= 7. Let's substitute these values into the Quadratic Formula.

a=- e±sqrt(e^2-4df)/2d

SubstituteValues

Substitute values

a=- ( -4)±sqrt(( - 4)^2-4( 1)( 7))/2( 1)

▼

Solve for a and Simplify

NegNeg

- (- a)=a

a=4±sqrt((- 4)^2-4(1)(7))/2(1)

NegBaseToPosBase

(- a)^2=a^2

a=4±sqrt(16-4(1)(7))/2(1)

Multiply

Multiply

a=4±sqrt(16-28)/2

SubTerm

Subtract term

a=4±sqrt(-12)/2

Since we cannot calculate the root of a negative number, there are no real solutions of the given equation.