# Let us construct the quadratic equations in one variable from the following statements.i. Divide 42 into two parts such that one part is equal to the square of the other part.ii. The product two consecutive positive odd numbers is 143.iii. The sum of the squares of two consecutive numbers is 313.

(i) Let one part be x.

And the other part = x2

Therefore, according to equation

x2 + x = 42

x2 + x – 42 = 0

(ii) Let the positive odd number be x + 1

The other consecutive positive odd number = (x + 1) + 2 = x + 3

According to question,

(x + 1)(x + 3) = 143

x2 + 3x + x + 3 = 143

x2 + 4x + 3-143 = 0

x2 + 4x -140 = 0

(iii) Let the first number be x.

And the other consecutive number = x + 1

According to question,

x2 + (x + 1)2 = 313

x2 + x2 + 1 + 2x = 313

2x2 + 2x + 1 – 313 = 0

2x2 + 2x - 312 = 0

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