Question

Asatoma sadgamaya tamasoma jyotirgamaya mrityorma amritam gamaya

Answer 1

ॐ असतो मा सद्गमय ।,तमसो मा ज्योतिर्गमय ।,मृत्योर्मा अमृतं गमय ।,ॐ शान्तिः शान्तिः शान्तिः ॥

इसका हिंदी में अर्थ है-

मुझे झूठ से सच्चाई का नेतृत्व करें, मुझे अंधेरे से प्रकाश तक ले जाएं, मुझे मृत्यु से अमरता तक ले जाएं ओम शांति शांति शांति।।



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Answer 2

Explanation:

f(x) = kx³ – 8x² + 5

Roots are α – β , α & α +β

Sum of roots = – (-8)/k

Sum of roots = α – β + α + α +β = 3α

= 3α = 8/k

= k = 8/3α

or we can solve as below

f(x) = (x – (α – β)(x – α)(x – (α +β))

= (x – α)(x² – x(α+β + α – β) + (α² – β²))

= (x – α)(x² – 2xα + (α² – β²))

= x³ – 2x²α + x(α² – β²) – αx² +2α²x – α³ + αβ²

= x³ – 3αx² + x(3α² – β²) + αβ² – α³

= kx³ – 3αkx² + xk(3α² – β²) + k(αβ² – α³)

comparing with

kx³ – 8x² + 5

k(3α² – β²) = 0 => 3α² = β²

k(αβ² – α³) = 5

=k(3α³ – α³) = 5

= k2α³ = 5

3αk = 8 => k = 8/3α

(8/3α)2α³ = 5

=> α² = 15/16

=> α = √15 / 4