+0

# plz help on trig question

+10
176
3
+389

Find the minimum possible value of $$\sqrt{58 - 42x} + \sqrt{149 - 140 \sqrt{1 - x^2}}$$  where $$-1 \le x \le 1$$

Apr 26, 2021

#1
+524
+5

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:)

Apr 26, 2021
#2
+2250
+2

I think there are more cases than just -1, 0, 1.

On desmos, the minumn is 10.44, when x = .131.

I'm not too sure how to do it tho. :((

=^._.^=

catmg  Apr 26, 2021
#3
+389
+3

thanks for the help guys

Apr 27, 2021