(a) Each side of a square is 4 m long. When each side isincreased by x m, the ar

Question

(a) Each side of a square is 4 m long. When each side isincreased by x m, the area is doubled. Find the value of x. (b) A positive real number is 1 more than its reciprocal. Findthe number. (a) Each side of a square is 4 m long. When each side isincreased by x m, the area is doubled. Find the value of x. (b) A positive real number is 1 more than its reciprocal. Findthe number.

Explanation / Answer

(a) A1 = (4 m)2 = 16m2 A2 = (4 + x)2 = 2(16) = 32 (4 + x)2 = 32 => 16 + 8x + x2 = 32 => x2 + 8x - 16 = 0 => x = [ -8 ± sqrt(82 - 4(1)(-16) ) ] / [ 2(1) ] => x = [ -8 ± sqrt( 128 ) ] / [ 2 ] => x = [ -8 ± 82 ] / [ 2 ] => x = (-4 - 42) or (42 - 4) => x ˜ -9.657 or 1.657 Final answer: x ˜ 1.657 m Check: (4 + 1.657)2 = 32.001649 ˜ 32 (b) x = 1 + 1 / x Since x does not equal zero, each term in the equation above can bemultiplied by x to get: x2 = x + 1 => x2 - x - 1 = 0 => x = [ -(-1) ± sqrt( (-1)2 - 4(1)(-1)) ] / [ 2(1) ] => x = [ 1 ± 5 ] / [ 2 ] => x = [ (1 - 5) / 2 ] or [ (1 +5) / 2 ] => x ˜ -0.618 or 1.618 Final answer: x ˜ 1.618 Check: 1 + 1 / 1.618 = 1.61804697 ˜ 1.618

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