If $p>q=p^2+q^3$ and $p<q=p^3-q^2$, then $(1>2)<3 = $
The problem defines two operations based on conditions:
- If $p > q$, then the operation (let's denote it by '>') results in $p^2 + q^3$.
- If $p < q$, then the operation (let's denote it by '<') results in $p^3 - q^2$.
We need to evaluate the expression $(1>2)<3$. The notation suggests that the symbol used directly determines the formula applied, potentially irrespective of the condition check for the evaluation itself.
Evaluating $(1>2)$
In the expression $1>2$, the operator is '>'. We apply the formula associated with this operator:
Formula for '>': $p^2 + q^3$
Substitute $p=1$ and $q=2$: $1^2 + 2^3 = 1 + 8 = 9$
Let the result be $R = 9$.
Evaluating $R<3$
Now, we need to evaluate $R<3$, which is $9<3$. The operator is '<'. We apply the formula associated with this operator:
Formula for '<': $p^3 - q^2$
Substitute $p=9$ and $q=3$: $9^3 - 3^2 = 729 - 9 = 720$
Final Result
The value of the expression $(1>2)<3$ is 720.
Important Questions from Algebra
If 2x – y = 2 and xy = \(\frac{3}{2}\) , then what is the value of x 3– \(\frac{{{y^3}}}{8}\) ?
If (10a 3+ 4b 3) : (11a 3- 15b 3) = 7 : 5, then (3a + 5b) : (9a - 2b) =?
- If 4sin 2 θ = 3(1+ cos θ), 0° < θ < 90°, then what is the value of (2tan θ + 4sin θ - sec θ)?
The value of:
\(\frac{{\sin 23^\circ \cos 67^\circ + \sec52^\circ \sin38^\circ + \cos 23^\circ \sin 67^\circ + \rm cosec52^\circ \cos 38^\circ }}{{\rm cose{c^2}20^\circ - {{\tan }^2}70^\circ }}\)
If (x + y) 3+ 27(x - y) 3= (Ax - 2y)(Bx 2+ Cxy + 13y 2), then the value of A - B - C is:
