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1. If x 4 +1÷x 4 =47 Then find x 3 +1÷x 3 2.factorise: a 12 x 4 -a 4 x 12

1. If x4+1÷x4=47
Then find x3+1÷x3
2.factorise: a12x4 -a4x12

Grade:9

3 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
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Pooja
127 Points
4 years ago

a12x4 -a4x12
x4a4(x8 - a8)


Using a2-b2=(a+b)(a-b)


x4a4(x4 + a4)(x4 - a4)

x4a4(x4 + a4)(x2 + a2)(x2-a2)

x4a4(x4 + a4)(x2 + a2)(x + a)(x - a)

Pooja
127 Points
4 years ago
X⁴ + (1/x⁴) = 47
Adding and subtracting 2 on LHS,
x⁴ + (1/x⁴) + 2 - 2 = 47
[(x²)² + (1/x²)² + 2 × (1/x²) x²] = 47+2
( x² + 1/x² )² = 49
( x² + 1/x² )² = 7²
x² + 1/x² = 7 [only positive value considered]
x² + 1/x² + 2 - 2 = 7
x² + 2.x².1/x² + 1/x² = 7+2
(x + 1/x)² = 9
(x+ 1/x)² = 3²
x + 1/x = 3 [only positive value consideeed]
x³ + 1/x³ = (x+ 1/x)³ - 3.x.1/x(x + 1/x)
= (3)³ - 3(3)
= 27-9
=18

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