fill in the blanks with the numbers so that the statement is true
2,3,4,7
(_ + _)2 + _ x _ = 53
To solve the equation (_ + _)2 + _ x _ = 53, we need to fill in the blanks with the given numbers 2, 3, 4, and 7. Let's go step by step:
First, we need to determine the two numbers that will be added together and squared. To find them, we need to think about the multiplication part of the equation.
Since the equation results in 53, and the only multiplication in the equation is _ x _, the answer must be a two-digit number. Since the given numbers are all single-digit numbers, it means that the two numbers being multiplied must be 7 and 4, which equals 28.
Now we can rewrite the equation as ( _ + _ )^2 + 28 = 53.
Next, we need to find the two numbers that will be added together. We know that ( _ + _ )^2 will equal 25 since 28 - 3 = 25.
To find the numbers that make up 25 when squared, we can try different combinations. We could use either 4 and 3, or 5 and 0.
If we choose 4 and 3, the equation would be (4 + 3)^2 + 28 = 53, which simplifies to 7^2 + 28 = 53. Here, 7^2 equals 49, and adding 49 to 28 gives us 77, not 53.
However, if we choose 5 and 0, the equation would be (5 + 0)^2 + 28 = 53, which simplifies to 5^2 + 28 = 53. Here, 5^2 equals 25, and adding 25 to 28 gives us 53, as required.
Therefore, the numbers that fill in the blanks are 5, 0, 2, 3, making the statement true.