Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Signal-flow graph wikipedia , lookup
System of polynomial equations wikipedia , lookup
Cubic function wikipedia , lookup
Elementary algebra wikipedia , lookup
Quartic function wikipedia , lookup
System of linear equations wikipedia , lookup
Quadratic equation wikipedia , lookup
(1) Radical Equations.notebook Solving Radical Equations A "radical" equation is an equation in which the variable is hiding inside a radical symbol (in the radicand). is a radical equation is NOT a radical equation To solve radical equations: 1. Isolate the radical (or one of the radicals) to one side of the equal sign. 2. If the radical is a square root, square each side of the equation. (If the radical is not a square root, raise each side to a power equal to the index of the root.) 3. Solve the resulting equation. 4. Check your answer(s) to avoid extraneous roots. Examples: 1. square both sides ( (2 x 1 = 4 x = 5 {5} 2 (1) Radical Equations.notebook Check: 2. √2x 1 = 3 2x 1 = 9 2x = 10 x = 5 isolate radical √2(5) 1 + 5 = 2 √10 1 + 5 = 2 √9 + 5 = 2 3+5=2 8=2 X x = 5 extraneous 3. 5√2x + 3 -5 = 40 Check: 5√2x + 3 = 45 add 5 √2x + 3 = 9 divide by 5 2x + 3 = 81square both sides 2x = 78 x = 39 {39} 4. ( ( 2 ( ( 5√2(39) + 3 - 5 = 40 5√78 + 3 - 5 = 40 5√81 - 5 = 40 5(9) - 5 = 40 45 - 5 = 40 40 = 40 2 square both sides x2 2x + 1 = 5x 9 x2 7x + 10 = 0 (x 5)(x 2) = 0 x = 5 x = 2 REMEMBER: A binomial squared: FOIL Quadratic: set = 0 and factor Check: 5 1 = √5(5) - 9 4 = √25 - 9 4 = √16 4=4 {2,5} 2 1 = √5(2) - 9 1 = √10 - 9 1 = √1 1=1 (1) Radical Equations.notebook 5. 5x + 3 = 3x + 7 2x + 3 = 7 2x = 4 x = 2 radical on both sides: square both sides Check: {2} √5(2) + 3 = √3(2) +7 √10 + 3 = √6 + 7 √13 = √13 6. Solve and check: the radical has a coefficient square the coefficient when squaring both sides {2,6} (1) Radical Equations.notebook 7. 2 ∛x + 9 = 3 (∛x 2 ( 3 3 + 9 = 3 since this equation has a cube root, raise each side the the third power x2 + 9 = 27 x2 = 18 x = ±√18 x = √9 √2 x = ±3√2 A check should be done!!