Question

If √13 - X√10= V8 + V5, then the value of x is
(1) 2
(2) 5
(3)- 4​

Answer 1

Option (3)

Step-by-step explanation:

Given :-

√(13 - X√10)= √8 + √5

To find :-

Find the value of x ?

Solution :-

Given equation is

√(13 - X√10)= √8 + √5

On squaring both sides then

[√(13 - X√10)]^2 = [√8 + √5]^2

=>13 - X√10= [√8 + √5]^2

=> 13 - X√10 = (√8)^2+(√5)^2+2(√8)(√5)

Since (a+b)^2 = a^2+2ab+b^2

=> 13 - X√10 = 8 + 5 + 2√40

=> 13 - X √10 = 13 + 2√(4×10)

=> 13 - X√10 = 13 +(2×2)√10

=> 13 - X√10 = 13 + 4√10

On Comparing both sides then

=> -X = 4

=> X = -4

Therefore ,X = -4

Answer:-

The value of X for the given problem is -4

Check :-

If X = -4 then

LHS =√( 13-X√10)

=>√( 13-(-4)√10)

=> √(13+4√10)

=>√(13+2√(2×2×10))

=> √(13+2√40)

=> √[(√8)^2+(√5)^2+(2)(√8)(√5)]

=> √[(√8)^2+(√5)^2]

=> √8+√5

=> RHS

LHS = RHS is true for X = -4

Used formulae :-

• (a+b)^2 = a^2+2ab+b^2