Question

please answer this question with process..find x.

Answer 1

(x² - 3x - 28)/x² - 49=3/17

=) (x² + 7x - 4x - 28)/x² - 7²=3/17

=) [x(x + 7) - 4(x+7)]/(x + 7) (x - 7)=3/17

=) (x + 7) (x - 4)/(x + 7) (x - 7)=3/17

=) (x - 4)/(x - 7)=3/17

=) 3(x - 7)=17(x - 4)

=) 3x - 21=17x - 68

=) 3x - 17x= -68+21

=) -14x= -47

=) x= 47/14

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Answer 2

Given x^2 - 3x - 28/x^2 - 49 = 3/17

On cross-multiplication, we get

(x^2 - 3x - 28) * 17 = (x^2 - 49) * 3

17x^2 - 51x - 476 = 3x^2 - 147

17x^2 - 51x - 476 - 3x^2 + 147

14x^2 - 51x - 329 = 0

We know that Quadratic Equation formula is -b+/root b^2 - 4ac/2a

 -b + root b^2 - 4ac/2a

= -(-51) + root (-51)^2 - 4(14)(-329)/2*14

= 7   ---- (1)

-b - root b^2 - 4ac

= -(-51)-root (-51)^2 - 4(14)-(329)/2*14

= -47/14.   ------ (2)


Final solutions are x = 7 and x = -47/14.

Since x = 7 doesn't satisfy the condition, The value of x will be x = -47/14.


Hope this helps!