Page 33 - 10-Math-2 THEORY OF QUADRATIC EQUATIONS

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4. x + y = a - b ; Version 1.1

5. x2 + (y - 1)2 = 10 ; x2 + y2 + 4x = 1
6. (x + 1)2 + (y + 1)2 = 5 ; (x + 2)2 + y2 = 5
7. x2 + 2y2 = 22 ; 5x2 + y2 = 29
8. 4x2 - 5y2 = 6 ; 3x2 + y2 = 14
9. 7x2 - 3y2 = 4 ; 2x2 + 5y2 = 7
10. x2 + 2y2 = 3 ; x2 + 4xy - 5y2 = 0
11. 3x2 - y2 = 26 ; 3x2 - 5xy - 12y2 = 0
12. x2 + xy = 5 ; y2 + xy = 3
13. x2 - 2xy = 7 ; xy + 3y2 = 2

2.7(ii) Solving Real Life Problems With Quadratic
Equations

There are many problems which can be lead to quadratic
equations. To form an equation, we use symbols for unknown
quantities in the problems. Then roots of the equation may provide
the answer to these problems.
The procedure to solve these problems is explained in the following
examples.

Example 1: Three less than a certain number multiplied by 9 less
than twice the number is 104. Find the number.

Solution: Let the required number be x. Then
three less than the number = x - 3
and 9 less than twice the number = 2x - 9
According to the given condition, we have
(x - 3) (2x - 9) = 104
2x2 - 15x + 27 = 104
2x2 - 15x - 77 = 0
Factorizing, we get

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