12.3 Write the first five terms of the sequence whose general term is
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Answer:
For the value of hypotenuse can be irrational, sum of squares of other two legs might be imperfect square number.
Step-by-step explanation:
We all know, the Pythagorean theorem can be stated as follows:
The sum of squares of two legs of a right angled triangle is equal to the square of the hypotenuse.
i.e.
Where, is the hypotenuse and
are the two other legs of the right angled triangle.
Given that:
and
are rational numbers.
To find:
Situation for which is irrational.
Square of a rational number is always rational.
So, both will be rational.
And sum of squares of two rational numbers will also be rational.
Therefore, will also be rational.
and
For the value of can be irrational, sum of squares of other two legs might be imperfect square number.