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4 years ago

Show work and solve for √ ( 5 x − 9 ) − 1 = x.

Mathematics

2 answers:

Mandarinka [93]4 years ago

4 0

sqrt (5x - 9) - 1 = x

sqrt(5x - 9) = x + 1

Square both sides:_

5x - 9 = x^2 + 2x + 1

x^2 - 3x + 10 = 0

(x - 5)(x + 2) = 0

x = 5 or -2.

Lets look for for any extraneous solutions:-

x = 5 ; sqrt (5*5-9) - 1 = sqrt16 - 1 = 3 and x = 3 (right hand side of equation)

so x = 5 is a solution

x = -2: sqrt(5*-2 - 9) - 1 = sqrt (-19) - 1 and x = -2 so this is extraneous

Answer:- One solution x = 5

Afina-wow [57]4 years ago

4 0

<u>Answer:</u>

x = -2 and x = 5

<u>Step-by-step explanation:</u>

$\sqrt{(5x-9)} -1=x\\\\\sqrt{(5x-9)}=x+1$

Taking square on both sides of the equation to get:

$(\sqrt{5x-9})^2=(x+1)^2\\\\5x-9=x^2+2x+1\\\\x^2+2x-5x+1+9=0\\\\x^2-3x+10=0$

Factorizing this equation to get:

$x^2+2x-5x+10=0\\\\x(x+2)-5(x+2)=0\\\\(x+2)(x-5)=0\\\\x=-2, x=5$

Checking for any extraneous solution:

Put x=-2 in the given expression:

$\sqrt{5(-2)-9} -1=-2\\\\\sqrt{-19}-1 \neq -2$ ---> extraneous solution

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Triangle 1 – ∠1 = 25°, ∠2 = 115° Triangle 2 – ∠1 = 25°, ∠3 = 40°
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Step-by-step explanation:

You can save yourself some trouble if you realize that one of the angles in one pair must match one of the angles in the other pair.

This observation eliminates the first two choices.

Going further, the triangles will be similar if the dissimilar angles together with one of the similar angles totals 180°.

Triangle 1 – ∠1 = 50°, ∠2 = 30°

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3 years ago

Identify the expression with nonnegative limit values. More info on the pic. PLEASE HELP.

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Answer:

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Step-by-step explanation:

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c) $\lim _{x\to 2}\:\frac{x-2}{x^2-2}=\frac{2-2}{\left(2\right)^2-2}=\frac{0}{4-2}=0$

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