The given equation is:
After rationalising the above equation, we get
by taking LCM we get the final answer.
Let 2root 3 / 5 be a rational no. in the form a/b where, a and b are integers.
2root3 / 5 = a / b
2root3 = 5a / b
root3 = 5a / 2b
Here. since a/b is a rational no., so 5a / 2b is also a rational no.
Hereby, root3 should also be a rational no.
But this contradicts tha fact that root3 is a rational no.
So, our assumption is wrong and hence 2root3 / 5 is an irrational no.
Explanation:lets assume that 2+root3 be rational
We know that root 3 is irrational where as 3 is rational
It not possible that a rational Is =to an irrational
Therefore,our asssumption is wrong
2+root3 is irrational
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if √3 is irrational then the whole no. is irrational
The solution is given in above picture I hope it will help you.....
yes, 2 root 3 upon 5 is irrational number
let us assume, number of pottery in a day = x
so, cost of production of each article = 2x + 3
as per question; x(2x + 3) = 90
or, 2x2 + 3x = 90
or, 2x2 + 3x – 90 = 0
or, 2x2 – 12x + 15x – 90 = 0
or, 2x(x – 6) + 15(x – 6) = 0
or, (2x + 15)(x – 6) = 0
hence, x = - 15/2 and x = 6
ruling out the negative value; x = 6
cost of article = rs. 15