Question

if a³ + b³ = 183, a²b + b²a = 182. then find : 9/5(a² - b²)?
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Answer 1

Step-by-step explanation:

a+b√b=183…………………(1)

a√b+b√a=182………………….(2)

Let. √a=x. and. √b. =y

x^3. + y^3 = 183……………….(3)

x^2.y + x.y^2 = 182

or. x.y(x+y) = 182………………….(4)

We know that

(x+y)^3=x^3+y^3+3.xy(x+y)

(x+y)^3= 183+3×182 = 183+546. = 729 = (9)^3

(x+y). = 9………………………(5)

on putting (x+y)=9 in eq.(4)

xy.(9)=182. or. xy = 182/9……………..(6)

Formula:-

x^2+y^2 =(x+y)^2. - 2xy……….(7)

On putting (x+y)=9. from eq.(5). and. xy = 182/9 from eq.(6)

x^2+y^2 = 81 -2×182/9. = (729–364)/9. = 365/9

On putting x^2=a. and. y^2. = b

a. +b. = 365/9………………….(8)

Now. 9/5.(a+b). = ( 9/5). × (365/9). = 73. Answer.

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