Question

Solve for x:

x^2-14x+49/x^2-49=3/17

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Answer 1

Step-by-step explanation:

Given :-

(x²-14x+49)/(x²-49) = 3/17

To find :-

Find the value of x ?

Solution :-

Given that

(x²-14x+49)/(x²-49) = 3/17

=> [(x)²-2(x)(7)+(7²)]/[(x)²-(7)²] = 3/17

We know that

(a-b)² = a²-2ab+b²

(a+b)(a-b) = a²-b²

Where, a = x and b = 7

Now,

=> (x-7)²/(x+7)(x-7) = 3/17

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

On cancelling (x-7) in both numerator and the denominator then

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

On applying cross multiplication then

=> 17(x-7) = 3(x+7)

=> 17x-119 = 3x+21

=> 17x-3x = 21+119

=> 14x = 140

=> x = 140/14

=> x = 10

Therefore, x = 10

Answer:-

The value of x for the given problem is 10

Check:-

If x = 10 then LHS of the given problem

=> (x²-14x+49)/(x²-49)

=> (10²-14×10+49)/(10²-49)

=> (100-140+49)/(100-49)

=> (149-140)/51

=> 9/51

=> (3×3)/(3×17)

=> 3/17

=> RHS

=> LHS = RHS is true for x = 10

Verified the given relations in the given problem.

Used formulae:-

→ (a-b)² = a²-2ab+b²

→ (a+b)(a-b) = a²-b²