Existence Code chef.

Posted on | Saturday, 20 May 2023 | No Comments

Problem

Chef has two variables $�$ and $�$. He wants to find out whether the variables satisfy the equation:

• ${�}^4+4\cdot {�}^2=4\cdot {�}^2\cdot �$

Input Format

• The first line of input will contain a single integer $�$, denoting the number of test cases.
• Each test case consists of two integers $�$ and $�$, as mentioned in statement.

Output Format

For each test case, output YES if the variables $�$ and $�$ satisfy the given equation, NO otherwise.

You may print each character in uppercase or lowercase. For example, Yes, YES, yes, and YeS are all considered the same.

Constraints

Sample 1:

5
2 2
4 4
3 6
8 32
200000000 20000000000000000

YES
NO
NO
YES
YES

Explanation:

Test case $1$: Given $�=2$ and $�=2$. Here, $2^4+4\cdot 2^2=4\cdot 2^2\cdot 2=32$.

Test case $2$: Given $�=4$ and $�=4$. Here, $4^4+4\cdot 4^2=320$ which is not equal to $4\cdot 4^2\cdot 4=256$.

Test case $3$: Given $�=3$ and $�=6$. Here, $3^4+4\cdot 6^2=225$ which is not equal to $4\cdot 3^2\cdot 6=216$.

Test case $4$: Given $�=8$ and $�=32$. Here, $8^4+4\cdot 32^2=8192$ which is equal to $4\cdot 8^2\cdot 32=8192$.

Test case $5$: Given $�=2\cdot 10^8$ and $�=2\cdot 10^{16}$. Here, $(2\cdot 10^8{)}^4+4\cdot (2\cdot 10^{16}{)}^2=32\cdot 10^{32}$ which is equal to $4\cdot (2\cdot 10^8{)}^2\cdot (2\cdot 10^{16})=32\cdot 10^{32}$.

code

for i in range(int(input())):

    a,b=map(int,input().split())

    if (a**4)+4*b**2==4*a**2*b:

        print("YES")

    else:

        print("NO")

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