Question

If the sum of two numbers is √18 and their difference is √14 .if the smaller number is x and greater one is y and x m = y find the value of m.
pls answer fast !!!!

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

If the sum of two numbers is √18 and their difference is √14 .if the smaller number is x and greater one is y and x m = y find the value of m.

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

Here,

• smaller number = x
• greater number = y

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• x + y = √18 ..............(1)
• x - y = √14 ................(2)

$\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}$

• Value of x , y and m

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

• x + y = √18
• x - y = √14

__________________Subtract it's

➥ (y+y) = (√18 - √14)

➥ 2y = (√18-√14)

➥ y = (√18-√14)/2

Keep value in equ(1),

➥ x + (√18-√14)/2 = √18

➥ x = √18 - ( √18-√14)/2

➥ x = (2√18 - √18 + √14 )/2

➥ x = (√18 + √14)/2

Thus:-

• Value of x = (√18 + √14)/2
• Value of y = (√18-√14)/2

Now,Calculate,

➥ xm = y

Keep value of x and y ,

➥ m(√18 + √14)/2 = (√18 - √14)/2

➥ m = [ (√18 - √14)/2] / [(√18 + √14)/2]

➥ m = (√18 - √14)/(√18+√14)

Rationalize denominator

➥ m = (√18 - √14)(√18-√14)/(√18+√14)(√18-√14)

➥ m = [(√18)² + (√14)² - 2.(√18).(√14)]/[(√18)²-(√14)²]

➥ m = [18 + 14 - 2. √(2×3×3×2×7)]/[(18-14)]

➥ m = (32 - 2.2.3.√7)/(4

➥ m = (32-12√7)/4

➥ m = 4(8-3√7)/4

➥ m = (8-3√7)

Hence:-

• Value of m = (8-3√7)

_____________________