I f space square root of u plus square root of v minus square root of w equals 0 comma space f i n d space t h e space v a l u e space o f left parenthesis u plus v minus w right parenthesis.

Asked by kishor.kp14 | 19th Jun, 2019, 09:41: AM

Expert Answer:

begin mathsize 16px style We space have comma
square root of straight u space plus space square root of straight v space minus space square root of straight w space equals space 0
rightwards double arrow square root of straight u space equals space square root of straight w space minus space square root of straight v space
Squaring space on space both space the space sides comma space we space get
rightwards double arrow straight u space equals space straight w space plus space straight v space minus space 2 square root of wv space space space space... space left parenthesis straight i right parenthesis space space space space space space space... space since space open parentheses straight a space minus space straight b close parentheses squared space equals space straight a squared space space plus space straight b squared space minus space 2 ab
Similarly comma
rightwards double arrow straight v space equals space straight w space plus space straight u space minus space 2 square root of wu space space space space... space left parenthesis ii right parenthesis space and space
square root of straight w space equals space square root of straight u space plus space square root of straight v
Squaring space on space both space the space sides comma space we space get
rightwards double arrow straight w space equals space straight u space plus space straight v space plus space 2 square root of uv space space space space space... space left parenthesis iii right parenthesis space space space...... space since space open parentheses straight a space plus space straight b close parentheses squared space equals space straight a squared space space plus space straight b squared space plus space 2 ab
To space find colon space straight u space plus space straight v space minus space straight w
From space left parenthesis straight i right parenthesis comma space left parenthesis ii right parenthesis space and space left parenthesis iii right parenthesis comma space we space get
space space straight u space plus space straight v space minus space straight w space equals space straight w space plus space straight v space minus space 2 square root of wv space plus space straight w space plus space straight u space minus space 2 square root of wu space minus space straight u space minus space straight v space minus space 2 square root of uv
space space space space space space space space space space space space space space space space space space space space equals space 2 straight w space space minus space 2 open parentheses square root of wv plus space square root of wu space plus space square root of uv close parentheses end style

Answered by Yasmeen Khan | 19th Jun, 2019, 10:39: AM