= frac{10 - 1}{10^{10}} = frac{9}{10^{10}} = 9 times 10^{-11}
Rule: If n is odd then a^n + b^n is divisible by a + b
Here n = 43 which is odd
a = 47 , b = 43
a + b = 47 + 43 = 90
So 47⁴³ + 43⁴³ is divisible by 90
Last verified on 12-08-2026
Given:
y = 2x
z = 5y
First find z in terms of x:
z = 5y = 5 _ (2x) = 10x
Now substitute in x + 3y + z:
x + 3y + z = x + 3_(2x) + 10x
= x + 6x + 10x
= 17x
Last verified on 05-08-2026
Solve:
Subtract 5 from both sides:
Divide by 2:
Use the formula: (a + b)(a − b) = a² − b²
Here, a = 3x and b = 2
= (3x)² − (2)²
= 9x² − 4
For the point (a,−a):
x=a,y=−a
Therefore:
y=−x
Last updated 27-07-2026 by NA
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