Question

In a single throw of two dice the probability of getting more than 7 is

Answer 1

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ANSWER

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\bf{QUESTION}QUESTION

Prove that if x and y are odd positive integers, then x²+y² is even but not divisible by 4.

\bf{step \: by \: step \: explanation}stepbystepexplanation

we know that any odd positive integer is of the form 2q+1 for some integer q.

so, let x = 2m+1 and y = 2n+1 for some integers m and n.

•°• x²+y²= ( 2m+1)²+(2n+1)²

==> x²+y²=4(m²+n²)+4(m+n)+2

==> x²+y²= 4{(m²+n²)+(m+n)} +2

==> x²+y² = 4q +2 , where q= (m²+n²)+(m+n)

==> x²+y² is even and leaves remainder 2 when divided by 4.

==> x²+y² is even but not divisible by 4.

HENCE PROVED✔✔

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