Solve-x-5-x-3-4-

Question Number 218088 by ArshadS last updated on 29/Mar/25

S o l v e

\sqrt{x + 5} + \sqrt{x - 3} = 4

Answered by A5T last updated on 29/Mar/25

\sqrt{x + 5} = u; \sqrt{x - 3} = v

u^{2} - v^{2} = 8 \land u + v = 4

\Rightarrow u - v = 2

\Rightarrow 2 u = 6 \Rightarrow u = 3 \Rightarrow v = 1

\Rightarrow x = 4

Answered by Rasheed.Sindhi last updated on 29/Mar/25

A n o t h e r w a y

l e t \sqrt{x - 3} = y \Rightarrow x = y^{2} + 3

\sqrt{y^{2} + 8} = 4 - y

y^{2} + 8 = y^{2} - 8 y + 16

8 y = 8 \Rightarrow y = 1

\sqrt{x - 3} = 1

x - 3 = 1 \Rightarrow x = 4

Answered by Rasheed.Sindhi last updated on 29/Mar/25

\sqrt{x + 5} + \sqrt{x - 3} = 4 \dots \dots . (i)

\sqrt{x + 5} - \sqrt{x - 3} = p (s a y) \dots (i i)

(i) \times (i i) : (x + 5) - (x - 3) = 4 p

p = 8 / 4 = 2

(i) + (i i) : 2 \sqrt{x + 5} = 4 + p = 4 + 2 = 6

x + 5 = 9

x = 4