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Find: a² + b² + c²

Albert

Well-known member
Jan 25, 2013
1,225
$\dfrac {1234567891011121314151617}
{7161514131211101987654321}=0.abc----$

please find :$a^2+b^2+c^2=? $

(use of computer is not allowed!)
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,725
Re: find :a^2+b^2+c^2=?

$\dfrac {1234567891011121314151617}
{7161514131211101987654321}=0.abc----$

please find :$a^2+b^2+c^2=? $

(use of computer is not allowed!)
Reminds me of this thread. First step is to check that numerator and denominator have the same number of digits (25). Then my little pocket calculator (assuming that I'm allowed to use it) gives the approximations as $$\frac{1234}{7161}\approx 0.1723,$$ $$\frac{12345678}{71615141} \approx 0.17238.$$ It looks as though the first three digits are $1,\ 7,\ 2$, with $1^2+7^2+2^2 = 54.$ I have not tried to prove this carefully as in that previous thread.
 

Albert

Well-known member
Jan 25, 2013
1,225
Re: find :a^2+b^2+c^2=?

$\dfrac {1234567891011121314151617}
{7161514131211101987654321}=0.abc----$

please find :$a^2+b^2+c^2=? $

(use of computer is not allowed!)
Let: $\dfrac{1234}{7162}<A=\dfrac {1234567891011121314151617}
{7161514131211101987654321}=0.abc----<\dfrac{1235}{7160}$

$0.1722<A<0.1725$

$\therefore a=1,b=7,c=2$

and $ a^2+b^2+c^2=54$