Consider the equation 3ˣ - 3ʸ = 3⁴ A solution to this equation with x and y integers
Solution:
3ˣ - 3ʸ = 3⁴ => 3ˣ - 3ʸ = 81
Now, we know
3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, 3⁵ = 243, 3⁶ = 729......
Clearly, as we increase the power, the difference becomes bigger.
There is no such x and y for which the difference becomes 81.
Hence, Option (d) is true.
The sum of squares of all the roots of the equation:
is:
One of the factors of 6x² – 24xy + 17x + 24y² – 34y + 5 is:
The cost of 2 pens and 5 pencils is ₹ 57. If the cost of a pen is increased by ₹ 1.50 and that of a pencil is decreased by ₹ 1, then the cost of 5 pens and 3 pencils is ₹ 109. What is the original cost of 3 pens and 4 pencils?
What is the remainder when the polynomial x¹⁰⁰ – 2x⁵¹ + 1 is divided by (x² – 1) ?
If x + = –1, then compute:
Let x be the greatest number which, when dividing 31, 61 and 91, leaves the same remainder. The LCM of x and 48 is:
The value of is
