3. Now consider equations of the form x-a=sqrt (bx+c) where a, b, and c are all positive integers and b > 1

(a) Create an equation of this form that has 7 as a solution and an extraneous solution. Give the extraneous solution.

(b) What must be true about the value of bx+c to ensure that there is a real number solution to the equation? Explain

Question

Mathematics

Delaney Marquez

10 August, 04:13

3. Now consider equations of the form x-a=sqrt (bx+c) where a, b, and c are all positive integers and b > 1

(a) Create an equation of this form that has 7 as a solution and an extraneous solution. Give the extraneous solution.

(b) What must be true about the value of bx+c to ensure that there is a real number solution to the equation? Explain

+2

Answers (1)

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Luca · Answer 1

X - a = sqrt (bx + c)

By using a = 5, b = 2/7, c = 2

We can have an equation where the solution is 7

X - 5 = sqrt (2/7 x + 2)

(x - 5) ^2 = 2/7 x + 2

X2 - 10x + 25 = 2/7 x + 2

X2 - 72/7 x + 23 = 0

X = 7

X = 23/7

b. the value of bx+c must be positive so that there is a real number solution