Question

5/7x-3=3/9x-5 solve the given equation

Answer 1

$\large\bigstar{\pmb{\sf Solution }}$

$:\implies\sf\dfrac{5}{7x-3} = \dfrac{3}{9x-5}$

$:\implies \sf 5(9x-5)=3(7x-3)$

$:\implies\sf 45x-25=21x-9$

$:\implies \sf 45x-21x=25-9$

$:\implies\sf 24x=16$

$:\implies \sf x=\dfrac{16}{24} =\bf\red{\dfrac{2}{3} }$

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Answer 2

Given :-

$\frac{5}{7x - 3} = \frac{3}{9x - 5}$

To Find :-

The value of "x" respectively .

Used Concepts :-

• Cross Multiplication Method.
• A general Quadratic equation is in the form of " ax² + bx + c = 0 ".
• If D = 0 , then two equal and real roots exists .
• If D > 0 , Then two real and different roots exists
• If D < 0 , Then two complex roots exists .
• If D is a perfect square value , Then the roots are real and rational .
• 0/x = 0 ( x € N ).

Solution :-

Note :- I will solve the question with two different methods and the answer of both methods is different but correct . Because we convert the given Equation in such a manner that we get two values of "x" by 2md method.

1st Way :-

$\frac{5}{7x - 3} = \frac{3}{9x - 5}$

By Cross Multiplication Method ,

$5 \times (9x - 5) = 3 \times (7x - 3)$

$45x - 25 = 21x - 9$

$45x - 21x = - 9 + 25$

$24x = 16$

$x = \frac{16}{24}$

$x = \frac{2}{3}$

Henceforth , The required answer is 2/3.

2nd Way :-

By 1st Way we get the following equation :-

24x = 16

24x - 16 = 0

Multiplying both sides by "x".

x × ( 24x - 16 ) = 0 × x

24x² - 16x = 0

Now , it is in the form of a quadratic equation , Where ,

a = 24 , b = -16 , c = 0

D = b² - 4ac = ( -16 )² - 4 × 24 × 0

=> 256 -0 = 256

√D = √256 = 16

Now By Quadratic formula ,

( x ) = -b + √D/ 2a , -b - √D/2a

=> - ( -16 ) + 16 / 2 × 24 , - ( -16 ) - 16 / 2 × 24

=> 16 + 16 /48 , 16 - 16 / 48

=> 32/48 , 0/48

=> 2/3 , 0

Hence , The required answers are 0 and 2/3 respectively.

We , can multiply the equation by x^n , where ( n € N ) , we always get one root as 2/3 and ( n - 1 ) roots as 0 always . Because the same as the degree of a polynomial is same as it's no. of roots . Therefore , we get one root as 2/3 and the other ( n - 1 ) roots as 0 because we take one root as 2/3.