x is a number such that when (x+1) 2 isdivided by (x-2) the quotient is 16 and t

Question

x is a number such that when (x+1) 2 isdivided by (x-2) the quotient is 16 and the remainder is (x-3) .What are the values of x?? Note: Answer Should be 3 or 12 x is a number such that when (x+1) 2 isdivided by (x-2) the quotient is 16 and the remainder is (x-3) .What are the values of x?? Note: Answer Should be 3 or 12

Explanation / Answer

(x + 1)2 / (x - 2) = 16 + (x - 3) / (x - 2) Division by zero is undefined, so (x - 2) does not equal zero. Multiply each term in the equation above by (x - 2) to get: (x + 1)2 = 16(x - 2) + (x - 3) => x2 + 2x + 1 = 16x - 32 + x - 3 => x2 + 2x + 1 = 17x - 35 => x2 + (2x - 17x) + (1 + 35) = 0 => x2 + -15x + 36 =   0 Solve for x by using the Quadratic Formula: x = [ -(-15) ± sqrt((-15)2 - 4(1)(36) ) ] / [ 2(1) ] => x = [ 15 ± 9 ] / [ 2 ] => x = 6 / 2    or   x = 24 / 2 => x = 3    or    x = 12

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