Toán Tiêng Anh!

Question

Recall that the iterated power abc denotes a(bc). Given that x is a real number which satisfies the equation 22x+42x=42

 

 what is the value of √22x? 

 

(a) 2      (b) 4       (c) 8    (d) 16      (e) 32

 

 

Comments

Giuppppppppppppppp

Answer 1

We have 42x=(22)2x=22.2x=(22x)2.
So 22x+42x=22x+(22x)x=42⇔22x+(22x)2−42=0
Change variable: 22x=t(t>0) we have: t2−t−42=0⇔(t+7)(t−6)=0
                                                                                      ⇔[t+7=0t−6=0⇔[t=−7t=6
So: t=22x=6.

Comments

Thank you very very very much!

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You are welcome!