Question

If (x - 5)' +(x-6)' +(x - 7) = 3(x - 5)(x-6)(x - 7), + then what is the value of x?​

Answer 1

Answer:

Solution

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(x−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

Step-by-step explanation:

hope it is helpful for you

Answer 2

Step-by-step explanation:

(x−5)(x−7)(x+6)(x+4)=504{(x−5)(x+4)}{(x−7)(x+6)}=504(x2−x−20)(x2−x−42)=504

Put x2−x=t

(t−20)(t−42)=504t2−62t+840=504t2−62t+336=0t2−6t−56t+336=0t(t−6)−56(t−6)=0(t−56)(t−6)=0t=56,6x2−x=t

For t=56

x2−x=56x2−x−56=0x2−8x+7x−56=0x(x−8)+7(x−8)=0(x+7)(x−8)=0