Q4 of 34 Page 178

Natural numbers, their netiaves and zero are together called intergers. How many pairs of integers are there, satisfying the equation, x2 + y2 = 25 ?

We have to find how many pairs of integers are there, satisfying the equation, x2 + y2 = 25

When x = 0, 0 + y2 = 25 so, y = + 5,-5


Same will be for when y = 0, x2 + 0 = 25 so, x = 5,-5


By hit and trial we can also find 9 + 16 or 16 + 9 = 25


So, x = 3,-3,4,-4 and respective y = 4,-4,3,3


So pairs are (0,5),(0,-5),(5,0),(-5,0),(3,4),(-3,4),(4,3),(4,-3),(-4,-3),(-3,-4).


More from this chapter

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2

In each of the following equations, take x as the given numbers and compute the numbers y.

y = x3 + x2 + x + 1, x = –1

 3

For a point starting at a point P and travelling along a straight line, time of travel is taken as t and the distance from P as s. The relation between s and t is found to be s = 12t – 2t2, there distances to the right are taken as positive numbers and to the left as negative numbers.

(i) Is the position of the point to the right or left of P, till 6 seconds?


(ii) Where is the position at 6 seconds?


(iii) After 6 seconds?


Here it is convenient to write 12t – 2t2 = 2t(6 – t).

 1

In the equation take z as the numbers and compute y.

 2

In the equation take x = –2 and and compute y.