Question

If x + 2y = m, where x<200, y is greatest one-digit perfect square
number, x is any prime number and mis a perfect square number,
then number of possible solutions is
5
6
4
3​

Answer 1

Answer:

4

Step-by-step explanation:

$x + 2y = m$

Here,

$x < 200$

y is the greatest one digit perfect square number

$y = 9$

$x + 2(9) = m$

$x + 18 = m$

x is any prime number, m is a perfect square number

If

$x = 7$

7 is a prime number.7<200

$7 + 18 = m$

$m = 25$

25 is a perfect square number

31 is a prime number.31<200

If

$x = 31$

$31 + 18 = m$

$m = 49$

49 is perfect square number

103 is a prime number. 103<200

$103 + 18 = m$

$m = 121$

$[/tex]</p><p>121 is a perfect square number</p><p></p><p>151 is a prime number. 151<200</p><p>[tex]151 + 18 = m$

$m = 169$

169 is a perfect square number.

The possible numbers are 7, 31,103,157

Answer 2

The number of possible solutions is: 4.

Step-by-step explanation:

Given:

• y is the greatest one digit perfect square number.
• x is a prime number. (x<200)
• m is a perfect square number.
• x +2y =m

Perfect square number- A number made by squaring a whole number.

                  Example:   1 =1x1,  4 =2x2, 9=3x3, 16=4x4.

• 9 is the greatest one digit perfect square, therefore y =9.

• x + 2y = m

    → x + 2(9)= m

    → x + 18 = m

x is a prime number and m is a perfect square.

Using Hit and trial method,

If x = 3 (x<200)

x + 2y = m

3+ 18 =21

21 is not a perfect square.

If x =7 (x<200)

x + 2y = m

7 + 18 =25

25 is a perfect square.

If x =11 (x<200)

x + 2y = m

11 + 18 =29

29 is not a perfect square.

If x =31 (x<200)

x + 2y = m

31 + 18 =49

49 is  a perfect square.

If x =103 (x<200)

x + 2y = m

103 + 18 = 121

121 is a perfect square.

If x = 151 (x<200)

x + 2y = m

151 + 18 =169

169 is  a perfect square.

The number of possible solutions 4.

x = 7, 31, 103, 151.

m = 25, 49, 121, 169.

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