How do extraneous solutions arise from radical equations?

2 answers:

5 0

In general, extraneous solutions arise when we perform non-invertible operations on both sides of an equation. (That is, they sometimes arise, but not always.) ... Solvingequations involving square roots involves squaring both sides of anequation. I hope that this helps you out, Have a wonderful day!!

eduard2 years ago

3 0

In general, extraneous solutions arise when we perform non-invertible operations on both sides of an equation

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Explain why x and 4x - 10 are factors of the expression x(4x - 10)3 rather than terms of the expression. What are the terms of t

andriy [413]

Solution :- Let p(x) be the polynomial such that

$p(x) = x(4x-10)^3\\\text{and let f(x) be another polynomial such that }\\f(x)=4x-10\\\text{To find , Put } f(x)=0\\\Rightarrow4x-10=0\\\Rightarrow4x=10\\\Rightarrow x=5/2\\\text{Now substituting value of x in p(x),we get}\\p(x)=\frac{5}{2} .(4(5/2)-10)^3\\\Rightarrow\frac{5}{2}.(10-10)^3=0\\\text{Similarly let g(x)=x ,we get x=0 by putting g(x)=0}\\\text{now f(x)=0 for x=0}\\\text{So by Factor theorem f(x) and g(x) are the factors of polynomial p(x)}\\$

$\text{Now} p(x) = x(4x-10)^3\\=64x^4-480x^3+1200x^2-1000x\\\text{so the terms of terms of } p(x) \text{are} 64x^4,-480x^3,1200x^2,-1000x\\\text{here, by using Factor theorem x is a factor of all the terms but 4x-10 is not. }$

$\text{And the terms of the factor 4x-10 are 4x and -10}$

3 0

3 years ago

Factor the trinomial below. x2 - 12x+ 35

lisabon 2012 [21]

Answer:

Step-by-step explanation:

x2 - 12x+ 35 = x^2 - 7x -5x +35

= x ( x-7) - 5(x - 7)

= (x-7)(x-5)

7 0

2 years ago

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100 points. Find the surface area of the triangular prism. The unit is cm^2

nikklg [1K]

First we find the area of the two triangles on each side (keep in mind that they are equal/congruent to each other):

(24*10)/2 = 120 cm^2

Then you find the areas of the three rectangles that are left:

24*19 = 456 cm^2
26*19 = 494 cm^2
10*19 = 190 cm^2

Finally, to find the surface area of the prism:

120+120+456+494+190 = 1,380 cm^2

6 0

2 years ago

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Robert wants to install windows in a bus barn to improve the airflow in the summer months. If Robert makes his own screens, he c

DedPeter [7]

=1/2

you add both on each side then subtract 2 from you anser

8 0

2 years ago

LMNO is a parallelogram. If NM = x + 15 and OL = 3x + 5, find the value of x

Sidana [21]

LMNO is a parallelogram
so NM = OL
x + 15 = 3x + 5
solve for x
x - 3x = 5 - 15
-2x = -10
x = 5

Answer
x = 5

5 0

3 years ago

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