Japanese | Can You Solve This? | Math Olympiade.

[@ElvisSaturn]

7+2√ 10 = a+b+2√ (a.b) -> a+b=7 and a.b=10 -> (a,b)={(2,5),(5,2)}

[@Teachbajrangi]

By squaring

[@TahminaNasrin-z2n]

inverse trigonometry pls

[@pedrojose392]

(2,5) or (5,2)

[@leonznidarsic]

a=5 b=2

[@ShriH-d1o]

Let >
7+2√10 =x²;=> x=√a+√b
7-2√10=y²; => y=√a- √b
x²y²=49-40=9; xy=±3;
Also x²+y²=14; x+y=2√a
& x- y=2√b; (x+y)²= x²+y²±2xy=14±6=20; 8
(2√a)²=20 or 8; √a=20/4 or 8/4; √a=(5 ; 2),✓ ( x-y)²=(2√b)²=
{14-/+(6)}; ,=>√b=(2; 5)
√a= (5, 2); √b= (2, 5)