SSC CGL Tier II 1 Dec 2016 Paper 1

Question : 8 of 100

Marks: +1, -0

The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of squares of the numbers is

Validate

Solution:

(2) Let three positive integers be x, y and z.
According to the question,

x + y + z = 18 ..... (i)

xyz = 162 ..... (ii)

and

x + y = z ..... (iii)

From equation (i),

z + z = 18 ⇒ 2z = 18 ⇒ z = 9

∴ xyz = 162

⇒

xy × 9 = 162

⇒ x y= {162}/{9}=18..... (iv)

∴(x-y)^{2}=(x+y)^{2}-4 x y

=(9)^{2}-4 × 18

=81-72=9

∴ x-y=3

∴ x+y+x-y=9+3

⇒ 2 x=12 ⇒ x=6

∴ x+y+z=18

⇒ 6+y+9=18

⇒ y=18-15=3

∴x^{2}+y^{2}+z^{2}

=(6)^{2}+(3)^{2}+(9)^{2}

=36+9+81=126

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