Solve each equation. See Examples 5 and 6.
51.Concept Check Consider the following “solution.”WHAT WENT WRONG?
Square each side.
Combine terms.
Subtract 9.
Divide by 4.52.Explain how you can tell that the equation has no real number solution with-
out performing any algebraic steps.
Solve each equation. See Example 7.
Solve each equation. (Hint: In Exercises 67 and 68, extend the concepts to fourth root radi-
cals.) See Example 8.
Solve each problem.
69.The square root of the sum of a number and 4 is 5. Find the number.
70.A certain number is the same as the square root of the product of 8 and the number. Find
the number.
71.Three times the square root of 2 equals the square root of the sum of some number and 10.
Find the number.
72.The negative square root of a number equals that number decreased by 2. Find the
number.
24 x^2 + 24 x= 3 24 x^2 + 6 x= 2233 x^2 - 9 x+ 8 = 23 x 235 x^2 - 6 x+ 2 = 23 x23 x^2 = 238 + 7 x 23 x^2 = 238 - 7 x232 x= 235 x+ 2 234 x+ 3 = 232 x- 122 x+ 11 + 2 x+ 6 = 2 2 x+ 9 + 2 x+ 16 = 723 x+ 4 - 22 x- 4 = 2 21 - x+ 2 x+ 9 = 42 x+ 6 = 2 x+ 72 2 x- 4 = 2 x- 3223 x+ 3 + 2 x+ 2 = 5 22 x+ 1 + 2 x+ 4 = 32 x=- 8x= 104 x= 404 x+ 9 = 493 x+ 4 +x+ 5 = 4923 x+ 4 + 2 x+ 5 = 732 x- 2 =x- 2 22 x+ 4 =x+ 12 x+ 9 =x+ 3 2 x+ 3 =x- 922 x+ 4 =x 23 x+ 6 =x22 x+ 7 =x- 1 32 x+ 13 =x+ 926 x+ 7 - 1 =x+ 1 28 x+ 8 - 1 = 2 x+ 1212 x+ 12 + 10 = 2 x 24 x+ 5 + 5 = 2 x2 x+ 2 - 2 =x 2 x+ 1 - 1 =x22 x+ 1 =x- 7 23 x+ 10 = 2 x- 525 x+ 11 =x+ 3 25 x+ 1 =x+ 1SECTION 8.6 Solving Equations with Radicals 537