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QuestionIf (x−1,11)=(8,y+3)(x-1,11)=(8, y+3), find x+2y\sqrt{x+2y}. Options: (a) 5 (b) ±5\pm 5 (c) 17\sqrt{17} (d) 25

Studdy Solution

STEP 1

Assumptions1. The given equation is (x−1,11)=(8,y+3)(x-1,11)=(8, \mathrm{y}+3). We need to find the value of x+y\sqrt{x+ y}

STEP 2

From the given equation, we can equate the corresponding elements of the ordered pairs.
x−1=8x -1 =811=y+11 = y +

STEP 3

olve the first equation for x.
x=8+1x =8 +1

STEP 4

Calculate the value of x.
x=8+1=9x =8 +1 =9

STEP 5

olve the second equation for y.
y=11−3y =11 -3

STEP 6

Calculate the value of y.
y=11−3=8y =11 -3 =8

STEP 7

Now that we have the values for x and y, we can substitute these into the equation x+2y\sqrt{x+2 y} to find its value.
x+2y=9+2()\sqrt{x+2 y} = \sqrt{9 +2()}

STEP 8

implify the equation inside the square root.
x+2y=+16\sqrt{x+2 y} = \sqrt{ +16}

STEP 9

Calculate the value inside the square root.
x+2y=25\sqrt{x+2 y} = \sqrt{25}

STEP 10

Calculate the square root of25.
x+2y=25=5\sqrt{x+2 y} = \sqrt{25} =5The value of x+2y\sqrt{x+2 y} is5.

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