Question

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The number of positive integral Solutions of x2+95 (x+3)
28 x +25 iu
The number of Solutions of the system of equations given
e below is lai+l4l=1 x ² + y ² - a - caci,
Given lx?m2+5.50 does not have two distince real roots
the minimum value of 5lt milli​

Answer 1

Step-by-step explanation:

420 possible solution

(x1 +x2 +x3)(y1 + y2) = 77

7 * 11 = 77

or

11 * 7 = 77

case 1

x1 + x2 + x3 = 7    and y1 + y2 = 11

7 =

1+1+5 , 1+2+4 , 1+3+3 , 1+4+2 , 1+5+1 ,

2+1+4 , 2+2+3 , 2+3+2 , 2+4+2 ,

3+1+3, 3+2+2, 3+3+1 ,

4+1+2 , 4+2+1 ,

5+1+1  

= (15 possibles)

Similarly

11 = 1+10 , 2+9 , 3+8 , 4+7 , 5+6 , 6+5 , 7+4 , 8+3 , 9+2 , 10+1 (10 possible)

total = 15 * 10 = 150 possible solutions

Now case 2

x1+x2+x3 = 11 & y1+y2=7

11=1+1+9 , 1+2+8 , 1+3+7 , 1+4+6 , 1+5+5 , 1+6+4 , 1+7+3 , 1+8+2, 1+9+1 , 2+1+8 , 2+2+7, 2+3+6,2+4+5, 2+5+4, 2+6+3, 2+7+2,2+8+1,

3+1+7,3+2+6,3+3+5,3+4+4,3+5+3,3+6+2,3+7+1

+ so on till

8+1+2 , 8 +2+1 ,

9+1+1

=(9 +8+7+6+5+4+3+2+1) = 45 Possible solutions

y1 + y2 = 7

1+6 , 2+5 , 3+4 , 4+3 , 5+2 , 6+1 = 6 possible solutions

45 * 6 = 270 possible solutions

case 1 + case2

150 + 270 = 420 possible solutions

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