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Solving Radical Functions

Solving Radical Functions. 3.4. 2 x+ 7. Solve 3 = 3 . . EXAMPLE 1. Solve a radical equation. Write original equation . Cube each side to eliminate the radical. Simplify. Subtract 7 from each side. Divide each side by 2 . EXAMPLE 1. Solve a radical equation.

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Solving Radical Functions

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  1. Solving Radical Functions 3.4

  2. 2x+7 Solve 3 = 3.  EXAMPLE 1 Solve a radical equation Write original equation. Cube each side to eliminate the radical. Simplify. Subtract 7 from each side. Divide each side by 2.

  3. EXAMPLE 1 Solve a radical equation CHECK Check x = 10 in the original equation. Substitute 10 for x. Simplify. Solution checks.

  4. 2. ( x+25 ) = 4 3. (23 x –3 ) = 4 for Example 1 GUIDED PRACTICE Solve equation. Check your solution. 1.3√ x – 9 = –1 x = 512 ANSWER ANSWER x = 11 x = –9 ANSWER

  5. 2 Raise each side to the power . 3 EXAMPLE 3 Standardized Test Practice SOLUTION Write original equation. Divide each side by 4. Simplify. ANSWER The correct answer is C.

  6. Raise each side to the power . 4 3 EXAMPLE 4 Solve an equation with a rational exponent Solve (x + 2)3/4 – 1 = 7. Write original equation. Add 1 to each side. Apply properties of exponents. Simplify. Simplify. Subtract 2 from each side.

  7. 7. = –2 x1/5 – 2 3 for Examples 3 and 4 GUIDED PRACTICE Solve the equation. Check your solution. 8. (x + 3)5/2 = 32 5. 3x3/2 = 375 ANSWER x = 25 ANSWER x = 1 6. –2x3/4 = –16 9. (x – 5)5/3 = 243 x = 32 ANSWER x = 16 ANSWER 10. (x + 2)2/3 +3 = 7 x = 243 ANSWER ANSWER x = –10 or 6

  8. Solve x + 1 = 7x + 15  EXAMPLE 5 Solve an equation with an extraneous solution Write original equation. Square each side. Expand left side and simplify right side. Write in standard form. Factor. Zero-product property Solve for x.

  9. Check x = 7 in the original equation. Check x = –2 in the original equation. The only solution is 7. (The apparent solution –2 is extraneous.) ANSWER EXAMPLE 5 Solve an equation with an extraneous solution CHECK

  10. 12. 11.x – 1 10x + 9 = x + 3 x = 2 1 4 for Examples 5 and 6 GUIDED PRACTICE Solve the equation. Check for extraneous solutions ANSWER x = 9 x = 0,4 ANSWER

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