Advertisements
Advertisements
प्रश्न
`4^((x+1))+4^((1-x))=10`
उत्तर
`4^((x+1))+4^((1-x))=10`
⇒ `4^(x + 1) + 4 · 4^x, 4^(1 - x) = 4/(4^x)`
⇒ `4 · 4^x + 4/(4^x) = 10`
Let `4x` be y.
∴ `4y+4/y=10`
⇒`4y^2-10y+4=0`
⇒`4y^2-8y-2y+4=0`
⇒`4y(y-2)-2(y-2)=0`
⇒`y=2 or y=2/4=1/2`
⇒ `4^x=2 or 1/2`
⇒`4^x=2^2x=2^1 or 2^(2x)=2^-1`
⇒`x=1/2` or `x= -(1)/2`
Hence, `1/2` and `-(1)/2` are roots of the given equation.
APPEARS IN
संबंधित प्रश्न
Solve the quadratic equation x2 – 3(x + 3) = 0; Give your answer correct to two significant figures.
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and solve it to find the original cost of the books.
Check whether the following is quadratic equation or not.
`2x^2-sqrt(3x)+9=0`
In the following, determine whether the given values are solutions of the given equation or not:
x2 + x + 1 = 0, x = 0, x = 1
If x = 2/3 and x = −3 are the roots of the equation ax2 + 7x + b = 0, find the values of aand b.
Without solving, comment upon the nature of roots of the following equation:
2x2 + 8x + 9 = 0
Which of the following are quadratic equation in x?
`x^2-1/x^2=5`
`sqrt3x^2+10x7sqrt3=0`
`12abx^2-(9a^2-8b^2)x-6ab=0`
Solve :
x4 - 2x2 - 3 = 0
