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Question

i) x+3/x = 2x

Answer: x + 3 = 2

How is the answer wrong and rewrite the answer correctly

ii) The points (1,2) (5,A) and (A,7) all lie on a straight line. Find all possible values of A with all working out.

Answer 1

Find x:

(x + 3)/x = 2x

x + 3 = 2x²

2x² - x = 3

x² - 1/2x = 3/2

x² - 1/4x = 3/2 + (- 1/4)²

x² - 1/4x = 24/16 + 1/16

(x - 1/4)² = 25/16

x - 1/4 = 5/4

1st value of x:

x = 1/4 + 5/4, x = 6/4, x = 3/2

2nd value of x:

x = 1/4 - 5/4, x = - 4/4, x = - 1

Answer: x = 3/2, - 1

Proof (x = 3/2):

(3/2 + 3)/(3/2) = 2(3/2)

(3/2 + 6/2)/(3/2) = 6/2

(9/2)(2/3) = 3

18/6 = 3

3 = 3

Proof (x = - 1):

(- 1 + 3)/- 1 = 2(- 1)

2/- 1 = - 2

- 2 = - 2

Answer 2

x+3/x=2x

adding -x on both sides

3/x=x

x^2=3

ii))they lie on a straight line so the slope of the points 1,2 and 1,3 are equal

-4/(2-A)=[1-A]/-5

20=a^2-3a+2

a^2-3a-18=0

(a-6)(a+3)=0

a= -3 or 6