If x - 1/x = 1/2, then write the value of 4x^2 + 4/x^2 = ?
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Given: x-1/x = 1/2.
To find: 4x^2+4/x^2.
Solution: We can write 4x^2+4/x^2 as 4(x^2+1/x^2).
Thus, 4(x^2+ 1/x^2)
=4{((x-1/x)^2)+2}.
=4{(1/2)^2 + 2}.
=4{1/4 +2}.
=4{9/4}.
= 9.
To find: 4x^2+4/x^2.
Solution: We can write 4x^2+4/x^2 as 4(x^2+1/x^2).
Thus, 4(x^2+ 1/x^2)
=4{((x-1/x)^2)+2}.
=4{(1/2)^2 + 2}.
=4{1/4 +2}.
=4{9/4}.
= 9.
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