ICSE Class 10 Maths Word Problems: Quadratic Equations

Solution

Let the smallest integer be x, then the largest integer will be x + 1.

x(x + 1) = 306

x² + x - 306 = 0

(x−17)(x + 18) = 0

x = 17, x = −18 

Solution

Let the smaller number be x. Square of the larger number is 18x.

Sum of their squares is

x² + 18x = 208

(x + 26)(x−8) = 0 x = −26 or x = 8 … both are positive numbers 

Solution

Let x be an odd positive integer. 

Then an odd positive integer just greater than x is x + 2. 

So,

x² + (x + 2)² = 290

x² + 2x −143 = 0

(x + 13)(x - 11) = 0

x = −13 or x = 11 (integers are positive)