AP EAMCET202318 May 2023Morning ShiftMathematicsQuadratic EquationActual

If (3+ 2 )^6-(3- 2 )^6=a+b 2 , then a+b=

Options

A5220
B5230
C5240
D5250

Correct answer

A. 5220

Step-by-step solution

(3+ 2 )^6-(3- 2 )^6=a+b 2 ...(i) aligned & Let x=3+ 2 and y=3- 2 & x^2+y^2=9+2+6 2 +9+2-6 2 =22 & x^3+y^3=(3+ 2 )^3+(3- 2 )^3 aligned aligned =3^3+( 2 )^3+3 3 2 (3 & + 2 ) & +3^3-( 2 )^3-3 3 2 (3- 2 ) aligned aligned & =54+36=90 & (3+ 2 )^6-(3- 2 )^6=x^6-y^6 & = (x^3+y^3 ) (x^3-y^3 ) & =90(x-y) (x^2+y^2+x y ) & =90.2 2 (22+9-2) & =58 90 2 =5220 2 & b=5220 and a=0 & a+b=0+5220=5220 . aligned

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