5^x-1÷2^2x=5²×5³
solve this
Answers
Answer:
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{5}^{x + 1} + {5}^{2 - x} = {5}^{3} + 15
x+1
+5
2−x
=5
3
+1
{5}^{x + 1} + {5}^{2 - x} = 1265
x+1
+5
2−x
=126
{5}^{x} .5 + {5}^{2} . {5}^{ - x } =1265
x
.5+5
2
.5
−x
=126
{5}^{x} .5 + \frac{25}{ {5}^{x} } = 1265
x
.5+
5
x
25
=126
5y + \frac{25}{y} = 126 \: \: \: \: where \: {5}^{x} = y5y+
y
25
=126where5
x
=y
5 {y}^{2} + 25 = 126y5y
2
+25=126y
5 {y}^{2} - 126y + 25 = 05y
2
−126y+25=0
5 {y}^{2} - 125y - y + 25 = 05y
2
−125y−y+25=0
5y(y - 25) - 1(y - 25) = 05y(y−25)−1(y−25)=0
(y - 25)(5y - 1) = 0(y−25)(5y−1)=0
y - 25 = 0 \: \: \: or \: \: \: 5y - 1 = 0y−25=0or5y−1=0
y = 25 \: \: \: \: or \: \: \: \: y = \frac{1}{5}y=25ory=
5
1
{5}^{x} = 25 = {5}^{2} \: \: \: \: \: or \: \: \: \: \: {5}^{x} = {5}^{ - 1}5
x
=25=5
2
or5
x
=5
−1
x = 2 \: \: \: \: \: or \: \: \: \: \: x = - 1x=2orx=−1
Hence, 2 and -1 are the roots of the given equation....
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