Given {x∈R:√x+2>√8−x2} ∴ Defining the function x+2≥0⇒x≥−2....(i) and 8−x2≥0⇒x∈[−2√2,2√2]...(ii) Now, √x+2>√8−x2 ∴ Squaring on both sides, x+2>8−x2⇒x2+x−6>0
⇒(x+3)(x−2)>0⇒x∈(−∞,−3)∪(2,∞)....(iii)
∴ According to Eqs. (i), (ii) and (iii) ⇒x∈[2,2√2 ] ∴ Maximum value of x=2√2