Question

please help help help​

Answer 1

Step-by-step explanation:

Given :-

[√(x+4)+√(x-10)]/[√(x+4)-√(x-10)] = 5/2

To find :-

Find the value of x ?

Solution :-

Given that

[√(x+4)+√(x-10)]/[√(x+4)-√(x-10)] = 5/2

On applying Componendo dividendo

If a/b = c/d then (a+b)/(a-b) = (c+d)/(c-d)

=> [{√(x+4)+√(x-10)}+{√(x+4)-√(x-10)}]/[{√(x+4)+√(x-10)}- {(√(x+4)-√(x-10)}] =

(5+2)/(5-2)

=> [√(x+4)+√(x-10)+(x+4)-√(x-10)]/[√(x+4)+√(x-10)- √(x+4)+√(x-10)] = 7/3

=> [√(x+4)+√(x+4)] / [ √(x-10)+√(x-10)] = 7/3

=> 2√(x+4)/2√(x-10) = 7/3

=> √(x+4)/√(x-10) = 7/3

On squaring both sides then

=> [√(x+4)/√(x-10)]² = (7/3)²

=> (x+4)/(x-10) = 49/9

On applying cross multiplication then

=> 49(x-10) = 9(x+4)

=> 49x-490 = 9x+36

=> 49x-9x = 36+490

=> 40x = 526

=> x = 526/40

=> x = 263/20

Therefore, x = 263/20

Answer:-

The value of x for the given problem is 263/20

Used formulae:-

Componendo - dividendo rule :-

If a/b = c/d then (a+b)/(a-b) = (c+d)/(c-d)