Question

lines callinear points perpendicular ​

Answer 1

Answer:

Given that 3^(x+2) + 3^(–x) = 10

=> (3^x)(3^2) + 1/(3^x) = 10

=> 9(3^x) + 1/(3^x) = 10

Now, let 3^x = y

Therefore, the equation reduces to

9y + 1/y = 10

=> 9y² + 1 = 10y

=> 9y² –10y +1 = 0

=> 9y² –9y –y +1 = 0

=> 9y(y–1) –(y–1) = 0

=> (y–1)(9y–1) = 0

=> y = 1, 1/9

Now, y = 1 => 3^x = 1

=> 3^x = 3^0

=> x = 0

And y = 1/9 => 3^x = 1/9

=> 3^x = 3^(–2)

=> x = –2

Thus, we get the solution as x = 0, –2.

3^ (x+2) +1/ 3^ x =10

[(3^ (x+2)*3^x) +1]/ 3^ x =10

[(3^ (x+2)*3^x )+1] = 3^ x *10

{3^ 2(x+1)} +1= 3^x * (9+1)

{3^ 2(x+1)} +1= 3^x * 9+3^x*1

{3^ 2(x+1)} +1= 3^x * 3^2+3^x

{3^ 2(x+1)} +1= 3^(x+2) +3^x

{3^ 2(x+1)} -3^(x+2) = 3^x - 1

Take 3^(x+2) common: 3^(x+2) [3^x - 1] = [3^x - 1]

[3^x - 1] = 0 OR 3^(x+2) = 1

3^x = 1 → x = 0

3^(x+2) =3 ^0

Comparing powers

x+2 = 0 → x = -2

Hence x = {-2,0}

Jai MATHaadi!

Answer 2

Answer:

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Explanation:

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