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2 years ago

Solving radical equations How to solve radical equations

Mathematics

2 answers:

Dafna1 [17]2 years ago

8 0

Simplify radical expressions. If we combine these two things then we get the product property of radicals and the quotient property of radicals. These two properties tell us that the square root of a product equals the product of the square roots of the factors. no radicals appear in the denominator of a fraction.

lozanna [386]2 years ago

5 0

A radical equation is an equation in which a variable is under a radical. To solve a radical equation:

Isolate the radical expression involving the variable. If more than one radical expression involves the variable, then isolate one of them.

Raise both sides of the equation to the index of the radical.

If there is still a radical equation, repeat steps 1 and 2; otherwise, solve the resulting equation and check the answer in the original equation.

By raising both sides of an equation to a power, some solutions may have been introduced that do not make the original equation true. These solutions are called extraneous solutions.

Example 1

Solve equation.

Isolate the radical expression.

equation

Raise both sides to the index of the radical; in this case, square both sides.

equation

This quadratic equation now can be solved either by factoring or by applying the quadratic formula.

Applying the quadratic formula, equation

Now, check the results.

If equation, equation

If x = –5,

equation

The solution is equation or x = –5.

Example 2

Solve equation.

Isolate the radical expression.

equation

There is no solution, since equation cannot have a negative value.

Example 3

Solve equation.

Isolate one of the radical expressions.

equation

Raise both sides to the index of the radical; in this case, square both sides.

equation

This is still a radical equation. Isolate the radical expression.

equation

Raise both sides to the index of the radical; in this case, square both sides.

equation

This can be solved either by factoring or by applying the quadratic formula.

Applying the quadratic formula, equation

Check the solutions.

If x = 10, equation

So x = 10 is not a solution.

If x = 2, equation

The only solution is x = 2.

Example 4

Solve equation.

Isolate the radical involving the variable.

equation

Since radicals with odd indexes can have negative answers, this problem does have solutions. Raise both sides of the equation to the index of the radical; in this case, cube both sides.

equation

The check of the solution x = –15 is left to you.

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Degger [83]

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, what are the coordinates of point Q and R. But I would show how to solve this.

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If point Q is at ( $x_1,y_1$ ) and S at ( $x_2,y_2$ ) and R(x, y) divides QS in the ratio QR to RS is 3:5, The coordinates of R is:

$x=\frac{3}{3+5}(x_2-x_1)+x_1=\frac{3}{8}(x_2-x_1)+x_1\\ \\y=\frac{3}{3+5}(y_2-y_1)+y_1=\frac{3}{8}(y_2-y_1)+y_1$

Let us assume Q(−9,4) and S(7,−4)

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Two angles are complementary. the measure of ∠abc is x° and the measure of ∠dbc is (3x + 10)°. what is the value of x? enter you

Marta_Voda [28]

This problem can be expressed through the equation:
x+3x+10= 90

To solve it we subtract 10 on both sides
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Add x and 3x
→4x=80
And divide each side by 4
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2 years ago

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zepelin [54]

Answer:

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Step-by-step explanation:

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Factors of :

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