Question Bank - Equations - Set 1

• Q7) Find all integers a,b,c for a^2 = bc + 4 & b^2 = ca + 4

• Q8) Find all integers triplet for (a+1/b) (b+1/c) (c+1/a) = 2

• Q9) Find Maximum point (x,y) of curve x = e^x * y ?

• Q10) if a and b are roots of x^2 - x + 1 = 0 then find a^5 + b^5 ?

• Q11) Find non negative integer solutions for 7x + 2y + z = 56 ?

• Q12) Find Non negative integer solutions for x + 3y + z = 21 ?

• Q13) Find non negative integer solutions for 2x + 5y + z = 20 ?

• Q14) Find non negative integer solution of x + 2y + 3z = 100 ?

• Q15) Find all ordered pairs of real numbers (x,y) which satisfy 17 x^2 +2y^2 -10xy -6x = -2 ?

• Q16) If x^2 * y^3 = 8 , where x, y > 0. What is the minimum value of 4x + 3y ?

• Q17) If a^2 + ab + b^2 = 1. How many ordered pairs (a,b) satisfy, where a,b are integers ?

• Q18) If a^6 + b^6 is a prime number .If a and b are distinct integers ,then what is their sum ?

• Q19) If x + y = 1, then what is the value of x^3 + y^3 + 3xy ?

• Q20) How many integer values of x satisfy |x - 2| +|x + 3| + |5 - x| + |x - 8| < = 16 ?

• Q21) x^2 + 3x +2 = 0 have x and y are roots. Find x^13 + y^13 ?

• Q22) How many real values of x satisfy the equation 2 ] x [ +5 = 9 x ?
Where ] [ lowest integer greater than or equal to x ??

• Q23) If a + b + c + d + e = 8 and a^2 + b^2 + c^2 + d^2 + e^2 = 16 and maximum and minimum of e is M and m respectively, then (M + m) is
a) 0
b) 1
c) 2
d) 3
e) (M + m) > 3

• Q24) min value of (x^2 + 9x +18)/(x+2)

• Q25) If 1 + 2^x + 2^(2x+1) = y^2 then find all pairs of integers (x, y)

• Q26) If z^5 - 32 = (z - 2)(z^2 - pz + 4)(z^2 - qz + 4) then value of (p^2 + 2p) is ?

61

96

61

153

40

1

1