∫³-1 dx = [x]³-1 = 3 - (-1) = 4
Write 32 as a power of 2
2 x 2 x 2 x 2 x 2 = 32
So 32 = 2^5
Compare with the given equation
2^x = 32
2^x = 2^5
If the bases are the same, the powers must be equal
x = 5
Last verified on 23-08-2026
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
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