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Answer:
22/7 is rational number
Step-by-step explanation:
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Step-by-step explanation:
Solutions :-
1) 22/7
Reason :-
22/7 is a rational number because the decimal expansion of 22/7 is a terminating and recurring decimal.
2)
Given that
log (x+y)/5 =( 1/2) [log x+logy]
We know that
log a+ log b = log ab
=> log (x+y)/5 =( 1/2) log(xy)
We know that log a^m = m log a
=> log (x+y)/5 = log (xy)^1/2
=> log (x+y)/5 = log√(xy)
=> (x+y)/5 = √(xy)
On squaring both sides then
=>[ (x+y)/5]^2 = [√(xy)]^2
=> (x+y)^2/5^2 = xy
=> (x^2+y^2+2xy)/25 = xy
=> x^2+y^2+2xy = 25xy
=> x^2+y^2 = 25xy-2xy
=>x^2+y^2 = 23xy
=>( x^2+y^2)/xy = 23
=> (x^2/xy) +(y^2/xy) = 23
=>[(x×x)/xy] +[(y×y)/xy] = 23
=> (x/y)+(y/x) = 23
Therefore, (x/y)+(y/x) = 23
Hence, Proved.
Used formulae:-
- log a+ log b = log ab
- log a^m = m log a
- The decimal expansion of a rational number is non terminating and recurring decimal.
- (a-b)^2 = a^2-2ab+b^2
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