Latest self Aptitude Question SOLUTION: Find (a^2 + b^2) if a^3 - b^3 + ab = 35^2 a^3 - b^3 - 3ab = 1 Where a,b are positive integers

• Placement Papers
• /
• self

self Question Papers:

(#M40013724) SELF question Keep an EYE

Find (a^2 + b^2) if
a^3 - b^3 + ab = 35^2
a^3 - b^3 - 3ab = 1

Where a,b are positive integers

Vinay Sipani (11 years ago)

Unsolved Read Solution (2)

Is this Puzzle helpful?   (0)   (0) Submit Your Solution

Read Solution (2) :

M.R.kartheek  (11 years ago)

Ans:) 613..
a^3 - b^3 + ab = 35^2
a^3 - b^3 - 3ab = 1
by solving these two equations we can get ab = 306
and a^3 - b^3 = 919
Identity 1:
a^3 - b^3 = (a-b)^3 +3ab(a-b)
lets assume (a-b) = x and we got a^3 - b^3 = 919 and ab = 306
den x^3 - 0.x^2 +3(306)(x) = 919
by solving the equation one root is 1
so a-b = 1
Identity 2:
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
919 = (1)(a^2 + 306 + b^2)
919 - 306 = (a^2 + b^2)
therefore (a^3 - b^3) = 613...
enjoyyy....

Is this solution Helpfull? Yes (5) | No   

ANKIT CHAUDHARY  (11 years ago)

if a^3-b^3+ab=15^2
and a^3-b^3-3ab=1
then a=8 and b=7
and ans of a^2+b^2=113

Is this solution Helpfull? Yes | No (2)  

Please Login to Read Solution.