Will give brainiest to the first answer need asap
solve for x
sqrt{3x-1}+sqrt{5x-3}+sqrt{x-1}=2sq rt{2}

x=1

Step-by-step explanation:

Squaring on both sides we get

-----(A)

Expanding Left hand side we get

 =

 =

 =

Expanding Right Hand side

  =

 =

 =

Hence we have now (A) equal to

subtracting 8x from both sides

Adding 4 on both sides we get...

now squaring on both sides again

                                                                   ----------(B)

Left hand side:

  =

  =

Right hand side:

  =

  =

  =

Hence we have (B) equals to

Subtract from both sides

 ---(C)

Also

 =

 =

Hence (C) becomes

Squaring both sides

                                      -------(D)

Left Hand Side

=

=  

Right hand Side

=

=  

Hence (D) becomes

subtracting from both sides

-----(E)

Solving using factoring and trying for all the possible rational roots starting from x=1 , we get it satisfies at x=1 itself. Hence (x-1) is one of the factor

Hence (E) becomes

(E)= becomes

hence x =1 or x=33

the third factor and not be factorized

Checking our solution for x=1

hence true

Checking our solution for x=33

False

hence our answer is

x=1

452,489 to the nearest thousand is 452,000