Answer
Verified
37.2k+ views
\[\frac{a_{10} - 2a_{8}}{2a_{9}}\] = \[\frac{(\alpha^{10} - \beta^{10}) - 2(\alpha^{8} - \beta^{8})}{2(\alpha^{9} - \beta^{9})}\]
= \[\frac{\alpha^{8}(\alpha^{2} - 2) - \beta^{8}(\beta^{2} - 2)}{2(\alpha^{9} - \beta^{9})}\]
∵𝛼 is root of x² - 6x - 2 = 0 ⇒ 𝛼² - 2 = 6𝛼
[ and β is root of x² - 6x - 2 = 0 ⇒ ꞵ² - 2 = 6ꞵ]
= \[\frac{\alpha^{8}(6\alpha) - \beta^{8}(6\beta)}{2(\alpha^{9} - \beta^{9})} = \frac{6(\alpha^{9} - \beta^{9})}{2(\alpha^{9} - \beta^{9})}\] = 3
Recently Updated Pages
To get a maximum current in an external resistance class 1 physics JEE_Main
f a body travels with constant acceleration which of class 1 physics JEE_Main
If the beams of electrons and protons move parallel class 1 physics JEE_Main
Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main
Find the points of intersection of the tangents at class 11 maths JEE_Main
For the two circles x2+y216 and x2+y22y0 there isare class 11 maths JEE_Main
Other Pages
A convex lens is dipped in a liquid whose refractive class 12 physics JEE_Main
Identify which of the above shown graphs represent class 12 physics JEE_Main
The mole fraction of the solute in a 1 molal aqueous class 11 chemistry JEE_Main
Formula for number of images formed by two plane mirrors class 12 physics JEE_Main
How many grams of concentrated nitric acid solution class 11 chemistry JEE_Main
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main