Home
Class 12
MATHS
If m, n are positive integers and m+nsqr...

If `m`, `n` are positive integers and `m+nsqrt(2)=sqrt(41+24sqrt(2))`, then `(m+n)` is equal to

A

`5`

B

`6`

C

`7`

D

`8`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` We have `m+nsqrt(2)=sqrt(41+24sqrt(2))`
Squaring both sides, we get
`m^(2)+2n^(2)+2sqrt(2)mn=4a+24sqrt(2)`
`:.` On comparing we get
`m^(2)+2n^(2)=41`…….`(i)`
and `mn=12`…….`(ii)`
`:.` On solving `(i)` and `(ii)`, we get
`implies m^(2)+(2(144))/(m^(2))=41`
`impliesm^(4)=41m^(2)+288=0`
`implies (m^(2)-32)(m^(2)-9)=0`
`implies m^(2) ne 32`
`:. m^(2) =9 implies m =3` and `n=4`
Hence, `(m+n)=7`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

If a_n and b_n are positive integers and a_n+sqrt(2)b_n=(2+sqrt(2))^n ,t h e n(lim)_(x->oo)((a_n)/(b_n))= a. 2 b. sqrt(2) c. e^(sqrt(2)) d. e^2

If a_(n) and b_(n) are positive integers and a_(n)+sqrt2b_(n)=(2+sqrt2))^(n) , then lim_(nrarroo) ((a_(n))/(b_(n))) =

If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a rational number other than positive integers

If two positive numbers are in the ratio 3 + 2sqrt(2) : 3 - 2sqrt(2) , then the ratio between their A.M. and G.M. is

Let T , be the r^(th) term of an A.P. whose first term is a and common difference is d If for some positive integers m, n, m != n , T_(m) = 1/n and T_(n) = 1/m , then a - d equals

If a_(1), a_(2) …… a_(n) = n a_(n - 1) , for all positive integer n gt= 2 , then a_(5) is equal to

Let T_r be the rth term of an A.P., for r=1,2,3, If for some positive integers m ,n , we have T_m=1/na n dT_n=1/m ,t h e nT_(m n) equals 1/(m n)

If m and n(n > m) are positive integers, then find the number of solutions of the equation n|sinx|=m|cosx|' for x in [0,2pi]dot Also find the solution.

Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as a factor.