prove that √3 -√2 is a irrational numbers
Answers
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Let is rational number...
= p/q
=p/q +
={p+
}/q
=p+
Squaring bhs
2q²= (p+ q )²
2q²=p² + 3q² + 2 pq
2q²-3q² -p² = 2pq ×
-(p²+q²) / 2pq =
Which is not possible as irrational cant be equal to rational...
Hence there is contradiction.
Thus the given number is irrational.
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...Hope it helps....
Answer:
Let \sqrt{2} - \sqrt{3}
2
−
3
is rational number...
\sqrt{2} - \sqrt{3}
2
−
3
= p/q
\sqrt{2}
2
=p/q + \sqrt{3}
3
\sqrt{2}
2
={p+\sqrt{3}q
3
q }/q
\sqrt{2}q
2
q =p+\sqrt{3}q
3
q
Squaring bhs
2q²= (p+ \sqrt{3}
3
q )²
2q²=p² + 3q² + 2 \sqrt{3}
3
pq
2q²-3q² -p² = 2pq × \sqrt{3}
3
-(p²+q²) / 2pq = \sqrt{3}
3
Which is not possible as irrational cant be equal to rational...
Hence there is contradiction.
Thus the given number is irrational.