how i did it (very similar to the video): so we know that: a + b = 12 1/a + 1/b = 8 1) 1/b + 1/a = 8 multiply both sides by ab a + b = 8ab 2) 8ab = a + b = 12 8ab = 12 2ab = 3 3) a + b = 12 (a + b)^2 = 12^2 a^2 + 2ab + b^2 = 144 2ab = 3 a^2 + b^2 + 3 = 144 a^2 + b^2 = 141 solution: a^2 + b^2 = 141
how i did it (very similar to the video):
so we know that:
a + b = 12
1/a + 1/b = 8
1)
1/b + 1/a = 8
multiply both sides by ab
a + b = 8ab
2)
8ab = a + b = 12
8ab = 12
2ab = 3
3)
a + b = 12
(a + b)^2 = 12^2
a^2 + 2ab + b^2 = 144
2ab = 3
a^2 + b^2 + 3 = 144
a^2 + b^2 = 141
solution: a^2 + b^2 = 141
This is PERFECT!!!
S = 12 ;
S/P = 8 ; 12/P = 8 ; P = 12/8 = 1,5
a^2 + b^2 = S^2 - 2P = 144 - 3 = 141
💯
Wow. Smooth like milk!!! Well done Nonny.
Daalu Nnam.
How much time should it take to solve it for a 10th grader? (This is 8th grade question tho)
Depends on their skill level. but less then 90 seconds. For very good students it will be mental math.
did it under 30 secs:
here, 1/a + 1/b = 8
taking lcm, (b+a)/ab =8
we know, a+b = 12 so, 12/ab = 8
12/8 = ab
3/2 = ab... substitute ab in the formula,
a^2 + b^2 = (a+b)^2 - 2ab
= 12^2 - 2* 3/2
=144-3
141#
Perfect!
Happy New Year.
From Korea
16secomds
hahahaha
show workings or it didn't happen.
i got 141.02741519 idk if i did something wrong
May I see your working?