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GalinKa [24]
4 years ago
8

Solve the equation identify extraneous solutions

Mathematics
1 answer:
PIT_PIT [208]4 years ago
6 0

Answer:

Step-by-step explanation:

The goal to solving any equation is to have x = {something}.  That means we need to get the x out from underneath that radical.  It's a square root, so we can "undo" it by squaring.  Square both sides because this is an equation.  Squaring both sides gives you

x^2=-3x+40

Get everything on one side of the equals sign and set the quadratic equal to 0:

x^2+3x-40=0

Throw this into the quadratic formula to get that the solutions are x = 5 and -8.  We need to see if only one works, both work, or neither work in the original equation.

Does 5=\sqrt{-3(5)+40}?

5=\sqrt{-15+40} and

5=\sqrt{25}

and 5 = 5.  So 5 works.  Let's try -8 now:

-8=\sqrt{-3(-8)+40} and

-8=\sqrt{24+40} so

-8=\sqrt{64}

-8 = 8?  No it doesn't.  So only 5 works. Your choice is the third one down.

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In trapezoid ABCD, AC is a diagonal and ∠ABC≅∠ACD. Find AC if the lengths of the bases BC and AD are 12m and 27m respectively.
xz_007 [3.2K]

Answer:

Length of diagonal is 18 m

Step-by-step explanation:

Given in trapezoid ABCD. AC is a diagonal and ∠ABC≅∠ACD. The lengths of the bases BC and AD are 12m and 27m. We have to find the length of AC.

Let the length of diagonal be x m

In ΔABC and ΔACD

∠ABC=∠ACD      (∵Given)

∠ACB=∠CAD      (∵Alternate angles)

By AA similarity theorem, ΔABC~ΔACD

∴ their corresponding sides are proportional

\frac{x}{27}=\frac{12}{x}=\frac{AB}{CD}

Comparing first two, we get

⇒ \frac{x}{27}=\frac{12}{x}

⇒ x^2=27\times 12

⇒ x=\sqrt324=18

hence, the length of diagonal is 18 m



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Answer:

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Step-by-step explanation:

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