A² = AB
A² - B² = AB - B²
(A + B)(A - B) = B(A - B)
A + B = B
B + B = B
2B = B
2 = 1
OK, I'll try doing it with numbers
A = B = 1
A² = AB => 1*1 = 1*1 => 1
A² - B² = AB - B² => 1 - 1 = 1-1 => 0
(A + B)(A - B) = B(A - B) = (1+1)(1-1) = 1(1-1) =>true 0=0!!! (sure enough!)
1+1 = 1 False...
OK, now I'll try with a different number
A = B = 2
A² = AB => 2*2 = 2*2 => 4
A² - B² = AB - B² => 4 - 4 = 4-4
(A + B)(A - B) = B(A - B) = (2+2)(2-2) = 2(2-2) =>True
(2+2)(2-2)=>2*2 + 2*2 -2*2 - 2*2 = 0
2(2*2) = 4-4 = 0
2+2 = 2 False...
Like I said...
The line (A + B)(A - B) = B(A - B) only works because both sides are equal(and equal to zero).
taking it past that is impossible...
therefore the solution only has real answers if A and B = 0
the maths is fine, and can be solved, but like I said, it only has 1 possible real solution.
there are no imaginary solutions either, I just tried...
A² - B² = AB - B²
(A + B)(A - B) = B(A - B)
A + B = B
B + B = B
2B = B
2 = 1
OK, I'll try doing it with numbers
A = B = 1
A² = AB => 1*1 = 1*1 => 1
A² - B² = AB - B² => 1 - 1 = 1-1 => 0
(A + B)(A - B) = B(A - B) = (1+1)(1-1) = 1(1-1) =>true 0=0!!! (sure enough!)
1+1 = 1 False...
OK, now I'll try with a different number
A = B = 2
A² = AB => 2*2 = 2*2 => 4
A² - B² = AB - B² => 4 - 4 = 4-4
(A + B)(A - B) = B(A - B) = (2+2)(2-2) = 2(2-2) =>True
(2+2)(2-2)=>2*2 + 2*2 -2*2 - 2*2 = 0
2(2*2) = 4-4 = 0
2+2 = 2 False...
Like I said...
The fairytale maths starts here...
A² - B² = AB - B²
since A = B all that = 0
2b = b => 2*0 = 0...
The line (A + B)(A - B) = B(A - B) only works because both sides are equal(and equal to zero).
taking it past that is impossible...
therefore the solution only has real answers if A and B = 0
the maths is fine, and can be solved, but like I said, it only has 1 possible real solution.
there are no imaginary solutions either, I just tried...