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Flura [38]
3 years ago
12

Find the solution of the square root of the quantity of x plus 2 plus 4 equals 6, and determine if it is an extraneous solution.

Mathematics
2 answers:
almond37 [142]3 years ago
6 0

Answer with Explanation:

 \sqrt{x+2+4}=6\\\\ \sqrt{x+6}=6

Squaring Both sides

→x + 6 =36

→x +6 -6=36-6

→x=30

When we substitute , x=30 in the original equation ,we get

L H S

   =\sqrt{30 +6}\\\\=\sqrt{36}=\pm 6

One value is 6 and other is ,-6.

So, x=30, is not an extraneous solution.    

→→Secondly if your equation is

\sqrt{x} +2+4=6\\\\ \sqrt{x}+6=6\\\\ \sqrt{x}=6-6\\\\ \sqrt{x}=0\\\\ x=0

Substituting ,the value of x, in original equation

L H S

= 0 +2 +4

=6

=R HS    

So, x=0, is also not an extraneous solution.  

Or, if the equation is

\rightarrow \sqrt{x+2} +4=6\\\\\rightarrow \sqrt{x+2}=6-4\\\\\rightarrow \sqrt{x+2}=2\\\\ \text{squaring both sides}\\\\ x +2=4\\\\ x=4-2\\\\x=2

Substituting the value of ,x in original equation

LHS

=\sqrt{2+2}+4\\\\= \sqrt{4}+4\\\\=2 +4=6

=RHS

So, x=2 , is not an Extraneous Solution.  

morpeh [17]3 years ago
4 0

minus 4 both sides

square both sides

x+2=4
minus 2
x=2
 
<span>the answer is 
 x = 2; not extraneous</span>
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3 years ago
In the diagram shown of circle A, tangent MB is drawn along with chords BAC and BF . Secant MFE intersects BAC at G. It is known
mote1985 [20]

Answer:

  • arc BF = 76°
  • ∠M = 31°
  • ∠BGE = 121°
  • ∠MFB = 111°

Step-by-step explanation:

(a) ∠FBM is the complement of ∠FBC, so is ...

  ∠FBM = 90° -52° = 38°

The measure of arc BF is twice this angle, so is ...

  arc BF = 2∠FBM = 2(38°)

  arc BF = 76°

__

(b) ∠M is half the difference between the measures of arcs BE and BF, so is ...

  ∠M = (1/2)(138° -76°) = 62°/2

  ∠M = 31°

__

(c) arc FC is the supplement to arc BF, so has measure ...

  arc FC = 180° -arc BF = 180° -76° = 104°

∠BGE is half the sum of arcs BE and FC, so is ...

  ∠BGE = (1/2)(arc BE +arc FC) = (138° +104°)/2

  ∠BGE = 121°

__

(d) ∠MFB is the remaining angle in ∆MFB, so has measure ...

  ∠MFB = 180° -∠M -∠FBM = 180° -31° -38°

  ∠MFB = 111°

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16. It's basically the problem you started with, but just reversed.
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