Simplify :
4√(-4) + 5√(-9) – 3√(-16)
Answered Feb 05, 2023
\(4\sqrt{-4}+5\sqrt{-9}-3\sqrt{-16}\)
= \(4\sqrt{4\times-1}+5\sqrt{9\times-1}-3\sqrt{16\times-1}\)
= 4(2i) + 5(3i) - 3(4i)
= 8i + 15i - 12i
= 11i
Correct Answer - (i) `15/4` (ii) `50/7`
Correct Answer - (i)`(5)/(2)` (ii) 4 (iii)` (9)/(8)` (iv)` (5)/(2)` (v) 4 (vi)`(4)/(3)`
Correct Answer - (i)`sqrt(2)` (ii)`(1)/(sqrt(3))` (iii)`(sqrt(3))/(2)` (iv)`3sqrt(2)` (v)`(1)/(2sqrt(5))` (vi)`2sqrt(2)`
Correct Answer - `{:((i),(12+13i),(ii),(-1+7i),(iii),(-3+5i),(iv),"(11-9i)"),((v),(9+22i),(vi),28,(vii),(18-i),(vii),-7sqrt(3)i):}`
\(\sqrt{-16}+3\sqrt{-25}+\sqrt{-36}-\sqrt{-625}\) = \(\sqrt{16\times-1}+3\sqrt{25\times-1}+\sqrt{36\times-1}-\sqrt{625\times-1}\) = 4i + 3(5i) + 6i - 25i = 25i - 25i = 0
a3−b3=(a−b)(a2+ab+b2) a3+b3=(a+b)(a2−ab+b2) Given, (3x+2y)(9x2−6xy+4y2) =(3x)3+(2y)3 =27x3+8y3
\(\frac{a^2+6}{a^3-8}\) x \(\frac{2a^2-3a-2}{2a^2+9a+4}\) ÷ \(\frac{3a^2-11a-4}{a^2+2a+4}\) = \(\frac{(a+4)(a-4)}{(a-2)(a^2+2a+4)}\) x \(\frac{(2a+1)(a-2)}{(2a+1)(a+4)}\) x \(\frac{(a+2)^2}{(3a+1)(a-4)}\) = \(\frac{(a+2)^2}{(a^2+2a+4)(3a+1)}\)
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