Maths-

General

Easy

Question

Solve the radical equation $square root of 3 x minus 2 end root equals x minus 4$

hint Hint:

Rearrange the equation and then solve for x.

The correct answer is: x = 9

Complete step by step solution:
Here given equation is $square root of 3 x minus 2 end root equals x minus 4$
On squaring both the sides, we have $left parenthesis square root of 3 x minus 2 end root right parenthesis squared equals left parenthesis x minus 4 right parenthesis squared$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 3 x minus 2 equals x squared minus 8 x plus 16 end cell row cell not stretchy rightwards double arrow x squared minus 8 x plus 16 equals 3 x minus 2 end cell end table$
$table attributes columnspacing 1em end attributes row cell space space space space space space space space space space space space space space not stretchy rightwards double arrow x squared minus 8 x minus 3 x plus 16 plus 2 equals 0 end cell row cell not stretchy rightwards double arrow x squared minus 11 x plus 18 equals 0 end cell end table$
Now, this is a quadratic equation with a = 1, b = -11, c = 18
Roots can be found with, $x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
$x equals fraction numerator 11 plus-or-minus square root of 121 minus 4 cross times 1 cross times 18 end root over denominator 2 cross times 1 end fraction$
$x equals fraction numerator 11 plus-or-minus square root of 49 over denominator 2 end fraction$
$not stretchy rightwards double arrow x equals fraction numerator 11 plus-or-minus 7 over denominator 2 end fraction$
$not stretchy rightwards double arrow x equals 9 text or end text 2$
Here, on substitution in given original equation we get the value of x = 9.

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Solve the radical equation

Rearrange the equation and then solve for x.

The correct answer is: x = 9

Complete step by step solution:Here given equation is On squaring both the sides, we have Now, this is a quadratic equation with a = 1, b = -11, c = 18Roots can be found with, Here, on substitution in given original equation we get the value of x = 9.

Related Questions to study

Does a linear , quadratic , or exponential function best model the data ? Explain.

Does a linear , quadratic , or exponential function best model the data ? Explain.

The speed, v, of a vehicle in relation to its stopping distance, d, is represented by the equation v =3.57√d. What is the equation for stopping distance in terms of the vehicle’s speed?

The speed, v, of a vehicle in relation to its stopping distance, d, is represented by the equation v =3.57√d. What is the equation for stopping distance in terms of the vehicle’s speed?

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