# Find: a² + b² + c²

#### Albert

##### Well-known member
$\dfrac {1234567891011121314151617} {7161514131211101987654321}=0.abc----$

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

(use of computer is not allowed!)

#### Opalg

##### MHB Oldtimer
Staff member
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
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 $a^2+b^2+c^2=54$