Question

(x-5)(x+4)=(x-7)(x-6) solve the equation​

Answer 1

Step-by-step explanation:

−5)(x−7)(x+6)(x+4)=504

{(x−5)(x+4)}{(x−7)(x+6)}=504

(x

2

−x−20)(x

2

−x−42)=504

Put x

2

−x=t

(t−20)(t−42)=504

t

2

−62t+840=504

t

2

−62t+336=0

t

2

−6t−56t+336=0

t(t−6)−56(t−6)=0

(t−56)(t−6)=0

t=56,6

x

2

−x=t

For t=56

x

2

−x=56

x

2

−x−56=0

x

2

−8x+7x−56=0

x(x−8)+7(x−8)=0

(x+7)(x−8)=0

x=−7,8

For t=6

x

2

−x=6

x

2

−x−6=0

x

2

−3x+2x−6=0

x(x−3)+2(x−3)=0

(x+2)(x−3)=0

x=−2,3

so the values of x are −7,8,−3 and 2

Answer 2

Given :

(x-5) (x+4) = (x-7) (x-6).

To Find :

The value of x.

Solution :-

(x-5) (x+4) = (x-7) (x-6)

$\mapsto \: {x}^{2} + 4x - 5x - 20 = {x}^{2} - 6x - 7x + 42 \\ \\ \mapsto \: - x - 20 = - 13x + 42 \\ \\ \mapsto \: - x + 13x = 42 + 20 \\ \\ \mapsto \: 12x = 62 \\ \\ \mapsto \: x = \frac{62}{12} = \frac{31}{4}$

Answer :-

The  value of  x  is  31/4.