Question

if x>0 then prove that 2^x+2^-x-2 is positive?

Answer 1

$<marquee>꧁༺HᎬᏒᎬ Ꭵs ᎽᎾuᏒ ᎪᏁsᎳᎬᏒ!!!༻꧂</marquee>$

Given that x>0 and we have to prove

${2}^{x} + {2}^{x} - 2$

as a positive number.

So

Proof :-

${2}^{x} + {2}^{x} - 2$

$= {4}^{x} - 2$

$=> {4}^{x} = 2$

$=> {2}^{2x} = {2}^{1}$

Comparing Power

$2x = 1$

$x = 1 \div 2$

We have got the value of 'x' so we will put in question were 'x' is coming.

${2}^{1 \div 2} + {2}^{1 \div 2} - 2$

$= {4}^{1 \div 2} - 2$

$= \sqrt{4} - 2$

$= 2 - 2$

$= 0$

Hence we have proved that it is a positive number!!!

$<marquee>Hope u understand❤❤❤</marquee>$

$<marquee>Please mark me as brainliest❤❤❤</marquee>$