Question

solve and verify (x+1) (x-1)-5=x (x-2) -4​

Answer 1

Answer:

(x+1) (x-1) -5= x(x-2) -4

x²-x+x-1-5 = x²-2x-4

-1-5= -2x-4

-6 = -2x-4

2x = -4+6

2x = 2

x=2/2

x=1

Answer 2

$\sf{Solution}$

Given to solve :-

(x+1) (x-1)-5=x (x-2) -4

Multiply (x+1)(x-1)

It is in form of (a+b)(a-b) = a² - b²

∴ (x +1)(x-1) = x²-1²

So,

(x+1) (x-1)-5=x (x-2) -4

x² - 1 -5 = x(x-2) -4

x² -6 = x² -2x -4

Transpose all terms to LHS

x² - 6 - x² +2x +4 =0

Put like terms together

x² - x² +2x -6 +4 =0

2x - 6 + 4 =0

2x -2 =0

Transpose 2 to RHS

2x = 2

2x /2 = 2/2

x = 1

Verification:

Substuite value of x Should be equal to LHS=RHS

(x+1) (x-1)-5=x (x-2) -4

x = 1

(1+1) (1-1) -5 = 1(1-2)-4

2 × 0 -5 = 1 × -1 -4

0 -5 = -1 -4

-5 = -5

Since LHS = RHS

Verified