Question

27. Simplify : [5(8^1/3+27^1/3)^3)]^1/4

29. If a+b+c= 9 and ab + bc+ ca=26 then find a^2+ b^2 + c^2​

Answer 1

Step-by-step explanation:

27)

[5{(8^1/3 + 27^1/3)³}]^1/4

= [5(2 + 3)³]^1/4

= [5×5³]^1/4

= (5⁴)^1/4

= 5

29)

a + b + c = 9

ab + bc + ca = 26

We know,

(a + b + c)²=a² + b² + c² - ab - bc - ca

(9)² = a² + b² + c² - 1(ab + bc + ca)

81 = a² + b² + c² - 1(26)

81 = a² + b² + c² - 26

a² + b² + c² = 107

Answer 2

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$1.$

$[5{(8^1/3 + 27^1/3)³}]^1/4$

$= [5(2 + 3)³]^1/4$

$= [5×5³]^1/4$

$= (5⁴)^1/4$

$= 5$

$2.$

$a + b + c = 9$

$ab + bc + ca = 26$

$We \: know,$

$(a + b + c)²=a² + b² + c² - ab - bc - ca$

$(9)² = a² + b² + c² - 1(ab + bc + ca)$

$81 = a² + b² + c² - 1(26)$

$81 = a² + b² + c² - 26$

$a² + b² + c² = 107$