It Always Boils Down to a Number
If x = 3 + 7 2 , then find ( x − 3 ) 2 .
The answer is 7.
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2 solutions
Nicely done. To be honest, I solved this in 4 seconds! Too much of this done in 9th :P
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Same. Great minds think alike. :D
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Thank you :D
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@Krishna Ar – @Krishna Ar , how come you are in 10th & still 14?
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@Ameya Salankar – Hey , I was born in Nov/99. FYI, There are people who were born even in May 2000 in my class. SO, they've just turned 14 and I'm like 14.5 years old.
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@Krishna Ar – @Krishna Ar , interesting! This means there are people in your class that should have been 8th pass now but are 2 years ahead! Wow!
@Krishna Ar – When i passed 10th i was also 14.5 but you are still intelligent more
@Krishna Ar What is 9th?
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He refers to the 9th grade @Mardokay Mosazghi . In India, we call it 9 th standard.
I know that.
How u solve this,can u explain basic rule of rationalise
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@Amarsinh Patil , rationalisation means making the denominator a rational number. We usually multiply both - numerator & denominator, by the conjugate - that is, changing the sign in the middle of the same term.
wow its so easy bt i did nt know it ...
Can somebody explain me how this was rationalised......
Krishna pls tell me the solution
Nyc solution
good work !
Nicely trick
x(3 + sq.rt 7)=2 so 3x + x(sq.rt 7) = 2 ; so 9x sqd + 7 X sqd = 4 i.e 16 X sqd =4
so 4X=2 x=0.5 ; x-3 = -2.5; (x-3)sqd = (-2.5) sqd = 6.25
from sympy import sqrt from sympy.simplify.simplify import rad_rationalize from sympy import symbols
rad_rationalize(2,3+sqrt(7))
-> yields (-6 + 2*sqrt(7), -2)
x=symbols('x') (((-1/2.) (-6 + 2 sqrt(7))-3)**2).simplify()
-> yields 7.00000000000000
Yes, it took me longer than four seconds.
Write 2=(3+7^1/2)(3-7^1/2) and then its simple algebra. :)
Using 2 < 7 < 3 , It is simple to deduce that 6 2 < 3 + 7 2 < 5 2 . Hence, 3 − 8 < x − 3 < 5 − 1 3 and squaring this gives 8 > 9 6 4 > ( x − 3 ) 2 > 2 5 1 6 9 > 6 Since the answer has to be an integer between 6 and 8, ( x − 3 ) 2 = 7
When we rationalise x , we get -
3 + 7 2 × 3 − 7 3 − 7 = 3 − 7 .
Substituting x , we get,
( x − 3 ) 2 = ( 3 − 7 − 3 ) 2 = ( − 7 ) 2 = 7 .