Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2010MathematicsQuadratic Equation

If , , are such that + + =2 , ^2+ ^2+ ^2=6, ^3+ ^3+ ^3=8, then ^4+ ^4+ ^4 is

Options

  1. A5
  2. B18
  3. C12
  4. D36

Correct answer

B. 18

Step-by-step solution

We have, ( + + )^2= ^2+ ^2+ ^2+2( + + ) 4=6+2( + + ) + + =-1...(i) Also, ^3+ ^3+ ^3-3 =( + + ) ( ^2+ ^2+ ^2- - - ) 8-3 =2(6+1) 3 =8-14=-6 or, =-2...(ii) Now, aligned ( ^2+ ^2+ ^2 )^2 & = ^4+ ^4+ ^4 +2 ( ^2 ^2+ ^2 ^2+ ^2 ^2 ) aligned aligned &= ( ^4+ ^4+ ^4 )+2 [( + + )^2 . -2 ( + + )] aligned aligned ( ^4+ ^4+ ^4 )= & 36 -2 [(-1)^2-2(-2)(2) ]=18 aligned

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

If is the common root of the quadratic equations x^2-5 x+4 a=0 , x^2-2 a x-8=0 , where a R , then the value of ^4- ^3+68 is 2025If , are the roots of x^2-5 x-6 =0 and , are the roots of x^2-5 x-6 =0 , then + + + = 2025If , , are the roots of the equation x ^3+ px ^2+ qx + r =0 , then ( + )( + )( + )= 2025Let f(x)=x^2+2 b x+2 c^2 and g(x)=-x^2-2 c x+b^2, x R . If b and c are nonzero real numbers such that f(x)> g(x) , then | c b | lies in the interval 2025If x ^2-4 ax +5+ a >0 for all x R whenever a ( , ) , then 4 + = 2025If , , are the roots of the equation x^3-12 x^2+k x-18=0 and one of them is thrice the sum of the other two roots, then ^2+ ^2+ ^2-k= 2025The polynomial equation of degree 5 whose roots are the roots of the equation x^5-3 x^4-x^3+11 x^2-12 x+4=0 each increased by 2, is 2025If the difference of the roots of the equation x^2-7 x+10=0 is same as the difference of the roots of the equation x ^2-17 x + k =0 , then a divisor of k is 2025 Full Quadratic Equation list All Manipal MET PYQs