Question

Solve for x:

px² -(p² - q²)x -q² = 0

Solve by splitting the middle term.​

Answer 1

Answer:

Step-by-step explanation:

Heya Dear,

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Given,

 α and ß are the zeroes of polynomial x² - px + q.

In this quadratic equation,

Coefficient of x² ( a ) = 1

Coefficient of x( b ) = -p

Constant term ( c ) = q.

We have,

⇒ Sum of zeroes = -b/a

⇒ α + ß = - ( - p ) / 1

∴ α + ß = p.

⇒ Product of zeroes = c/a

⇒ αß = q/1 = q

Now,

⇒ ( α + ß )² = α² + ß² + 2 αß

⇒ ( p )² = α² + ß² + 2 q

⇒ p² = α² + ß² + 2 q

∴ α² + ß² = p² - 2q

Hope it helps

Answer 2

Answer:

pointed out that the modular equation function μ a (r ) and its solution ϕ K (a, r ) are the generalizations of the modulus μ(r ) of the Grötzsch ring in the plane and quasiconformal Hersch-Pfluger distortion function ϕ K (r ), respectively. Therefore, many important properties and inequalities for μ(r ) and ϕ K (r ) have been extended to μ a (r ) and ϕ K (a, r ) (see [2,4,5,27,28,40,42,44,58]). For instance, in 2007, Wang et al. [40] generalized Theorem 6 of [29] and found that ϕ K (a, r ) is related to m a (r ) + log r and μ a (r ) + log r (see Corollary 1.1). ...