How to solve square root equations?

We have removed one square root.

Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)

Simplify: 2x−5 = 2√(x−1) + x

Subtract x from both sides: x−5 = 2√(x−1)

Now do the "square root" thing again:

We have now successfully removed both square roots.

Let us continue on with the solution.

Expand right hand side: x−1 = (x2 − 10x + 25)/4

It is a Quadratic Equation! So let us put it in standard form.

Multiply by 4 to remove division: 4x−4 = x2 − 10x + 25

Bring all to left: 4x − 4 − x2 + 10x − 25 = 0

Combine like terms: −x2 + 14x − 29 = 0

Swap all signs: x2 − 14x + 29 = 0

Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:

2.53 and 11.47 (to 2 decimal places)

Let us check the solutions:

2.53: √(2·2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1! 

11.47: √(2·11.47−5) − √(11.47−1) ≈ 1 Yes that one works. 

There is really only one solution:

11.47 (to 2 decimal places)

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

answer is : muchas/tipicas

have a nice day!

~recklesschicken