Solve for x, given the equation square root of x plus 9 − 4 = 1.

Asked by maham237 @ 18/12/2020 in Mathematics viewed by 428 People

x = 16, solution is not extraneous

x = 16, solution is extraneous

x = 34, solution is not extraneous

x = 34, solution is extraneous

Answered by maham237 @ 18/12/2020

Remember that an extraneous solution of an equation is a solution that emerges from the algebraic process of solving the equation but is not a valid solution of the equation.

First, we are going to solve our equation algebraically:

Step 1 simplify the equation:

$\sqrt{x} +9-4=1$

$\sqrt{x}+ 5=1$

Step 2 subtract 5 from both sides of the equation:

$\sqrt{x} +5-5=1-5$

$\sqrt{x} =-4$

Step 3 square both sides of the equation:

$\sqrt{x} ^2=(-4)^2$

$x=16$

Next, we are going to replace our solution in our original equation and check if it is a valid solution:

$\sqrt{x} +9-4=1$

$\sqrt{16} +5=1$

$4+5=1$

$9\neq 1$

Since 9 is not equal to 1, $x=16$ is not valid solution of the equation; therefor it is an extraneous solution.

We can conclude that the correct answer is: x = 16, solution is extraneous

Solve for x, given the equation square root of x minus 5 + 7 = 11.

Asked by maham237 @ 25/12/2020 in Mathematics viewed by 379 persons

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