5. X +2z =2y 3} b? = ac T, IR , a2 b2गा अं... SNl e o S

1.	5. X +2z =2y 3} b? = ac T, IR , a2 b2गा अं... SNl e o S
Answer» Since x + z = 2y, z = 2y - x and: b^(z - x) = b^(2y - 2x) = (b^2)^(y - x) But b^2 = ac, so that becomes: b^(z - x) = a^(y - x) c^(y - x) a^(y - z) b^(z - x) c^(x - y) = a^(y - z + y - x) c^(x - y + y - x) = a^(2y - z - x) c^0 = a^(2y - z - x) But x + z = 2y also means 2y - z - x = 0, so the exponent on a is zero too a^(y - z) b^(z - x) c^(x - y) = a^(0) = 1 This, of course, requires a,b,c to be nonzero.

Answer»

Since x + z = 2y, z = 2y - x and: b^(z - x) = b^(2y - 2x) = (b^2)^(y - x)

But b^2 = ac, so that becomes:

b^(z - x) = a^(y - x) c^(y - x)

a^(y - z) b^(z - x) c^(x - y) = a^(y - z + y - x) c^(x - y + y - x) = a^(2y - z - x) c^0 = a^(2y - z - x)

But x + z = 2y also means 2y - z - x = 0, so the exponent on a is zero too a^(y - z) b^(z - x) c^(x - y) = a^(0) = 1

This, of course, requires a,b,c to be nonzero.

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