+428 Find the minimum possible value of \( \sqrt{58 - 42x} + \sqrt{149 - 140 \sqrt{1 - x^2}}\) where \(-1 \le x \le 1\)
+526 It is given that \(-1 ≤ x≤ 1\)
Case 1: when \(x=-1\)
\(\sqrt{58-42x}+\sqrt{149-140\sqrt{1-x^2}} = \sqrt{100}+\sqrt{149}\)
\(=10+7\)
\(=17\)
Case 2: when \(x=0\)
\(\sqrt{58-42x}+\sqrt{149-140\sqrt{1-x^2}}=\sqrt{58}+\sqrt9 \)
\(=7.6+3\)
\(=10.6\)
Case 3: when \(x=1\)
\(\sqrt{58-42x}+\sqrt{149-140\sqrt{1-x^2}}=\sqrt{16}+\sqrt{149}\)
\(=4+7\)
\(=11\)
Comparing cases 1, 2 and 3
Minimum value =10.6
∴ Minimum possible value of given expression is 10.6
~Hope you got it:)
