Question

b. Problem Solving.
1) The square root of the sum of two consecutive integers is 7. Find the two integers.
2) The square root of the sum of two consecutive odd integers is 6V2. Find the larger integer​

Answer 1

Answer:

1) 24 & 25

2) 37

Step-by-step explanation:

1) Let first number be x

So second number = x + 1

So, as per question,

$\sqrt{x + x + 1 } = 7 \\ \sqrt{2x + 1} = 7$

Now, on squaring both sides...

$2x + 1 = 49 \\ 2x = 49 - 1 \\ x = \frac{48}{2} \\ x = 24$

So the two integers are, 24 and 25.

2) Let one integer = x

And another = x + 2

So, as per question...

$\sqrt{x + x + 2} = 6 \sqrt{2} \\ = > \sqrt{2x + 2} = 6 \sqrt{2}$

Now squaring both sides...

$2x + 2 = 72 \\ 2x = 72 - 2 \\ x = \frac{70}{2} \\ x = 35$

So, Larger Integer = 35 + 2

= 37

Hope it helps!

Answer 2

Answer:

1) two integers are 24 and 25

2) larger integer is 37

Given problem:

1) The square root of the sum of two consecutive integers is 7. Find the two integers.

2) The square root of the sum of two consecutive odd integers is 6V2. Find the larger integer​

[ here in 2nd problem the number 6V2 is may be 6√2  

Step-by-step explanation:

1st problem

given that square root of the sum of two consecutive integers = 7

Let x and x+1 are be the two consecutive integers

from given data   $\sqrt{x+ (x+1)} = 7$  

do squaring on both sides

                      $(\sqrt{x+ (x+1)} )^{2} = 7^{2}$

                                  x + x + 1  = 49  

                                         2x  = 48

                                           x  = 24

the two integers are  24 and 25  

2nd problem

given that square root of the sum of two consecutive odd integers = 6√2  

Let  x and x+2 are be the two consecutive integers

from given data  $\sqrt{x+ (x+ 2) } = 6\sqrt{2}$  

do squaring on both sides  

                        $(\sqrt{x+ (x+ 2) } )^{2} = (6\sqrt{2})^{2}$

                                  x + x + 2  = 36(2)

                                            2x  = 72 - 2

                                             2x =  70

                                               x  = 35  

the two integers are 35 and 37

and the larger integer = 37