Question

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Answer 1

Answer:

22/7 is rational number

Step-by-step explanation:

23

Answer 2

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