For integers x and y define * by : x * y = (x + y)^2 — (x — y)^2 and x \triangle y = (x + y)^3 + (x - y )^3 Then (3 * 5 ) * (1 △ 2) =

TS ICET 23 May 2018 Shift 2 Paper

Question : 75 of 200

Marks: +1, -0

For integers x and y define * by :
x * y =

(x + y)^2 — (x — y)^2 and x △ y = (x + y)^3 + (x - y )^3

Then (3 * 5 ) * (1 △ 2) =

Solution:

x^{*} y=(x+y)^{2}-(x-y)^{2}

x ∆ y=(x+y)^{3}+(x-y)^{3}

(3×5)×(1∆2)

⇒[(3+5)^{2}-(3-5)^{2}]^{*}[(1+2)^{3}+(1-2)^{3}]

⇒[8^{2}-(-2)^{2}]^{*}[(3)^{3}+(-1)^{3}]

⇒[64-4]^{*}[27-1] ⇒ 60*26

⇒[(60+26)^2-(60-26)^2]

⇒[(86)^2-(36)^2]

⇒13×480

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