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## QUADRATIC EQUATION WORD PROBLEMS WORKSHEET WITH ANSWERS

Difference between a number and its positive square root is 12. Find the number.

If the difference between a number and its reciprocal is ²⁴⁄₅ , find the number.

Divide 25 in two parts so that sum of their reciprocals is ⅙ .

Its positive square root is √x.

Given : Difference between x and √x is 12.

x = 9 does not satisfy the condition given in the question.

Therefore, the required number is 16.

Then, its reciprocal is ¹⁄ y .

Given : D ifference between a number and its reciprocal is ²⁴⁄₅ .

Multiply both sides by 5y to get rid of the denominators y and 5.

Subtract 24y from boths sides.

Both the values y = 5 and y = ⁻¹⁄₅ satisfy the condition given in the question.

Therefore, the required number is 5 or ⁻¹⁄₅ .

Cost of one meter of the rod which is 2 meter shorter is

Given : If the rod was 2 meter shorter and each meter costs $1 more.

That is, 60/(x-2) is $1 more than 60/x.

Multiply both sides by x(x - 2) to get rid of the denominators (x - 2) an x.

x(x - 2) [⁶⁰⁄₍ₓ ₋ ₂₎ - ⁶⁰⁄ₓ] = x(x - 2)

x(x - 2) [⁶⁰⁄₍ₓ ₋ ₂₎] - x(x - 2) [⁶⁰⁄ₓ] = x(x - 2)

Because length can not be a negative number, we can ignore x = -10.

Therefore, the length of the given rod is 12 m.

Let x be one of the parts of 25.

Then, the other part is (25 - x). Given : Sum of the reciprocals of the parts is 1/6.

Multiply both sides by 6x(25 - x) to get rid of the denominators x, (25 - x) and 6.

6x(25 - x) [ ¹⁄ₓ + ¹⁄₍₂₅ ₋ ₓ₎ ] = 6x(25 - x) [⅙]

6x(25 - x) [ ¹⁄ₓ ] - 6x(25 - x) [ ¹⁄₍₂₅ ₋ ₓ₎ ] = x(25 - x)

Therefore, the two parts of 25 are 10 and 15.

Let x and (x + 4) be the lengths of other two sides. Using Pythagorean theorem, we have

x = -16 can not be accepted. Because length can not be negative.

Therefore, the other two sides of the triangle are 12 cm and 16 cm.

(x - 12), (x - 13) and (x - 14)

(x - 12) 2 = (x - 13) 2 + (x - 14) 2

x 2 - 24x + 144 = x 2 - 26x + 169 + x 2 - 28x + 196

x 2 - 24x + 144 = 2x 2 - 54x + 365

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