If log10[98 + √(x3-x2-12x+36)] = 2 , Then x = - Maths - Sets

Question

If log10​​​​[98 +
√(x3-x2-12x+36)] = 2 , Then x =??

Manbar Singh · Accepted Answer

log1098 + x3-x2-12x+36 = 2⇒98 + x3-x2-12x+36 = 102⇒98 + x3-x2-12x+36 = 100⇒x3-x2-12x+36 = 2⇒x3-x2-12x+36 = 4⇒x3-x2-12x+32 = 0Let px = x3-x2-12x+32 Put x = -4, we getp-4 = -43--42-12-4+32 = -64-16+48+32 = 0So, x + 4 is a factor of px
On dividing px by x+4, we get quotient = x2-5x+8 and remainder = 0Now, px = x+4x2-5x+8So, x3-x2-12x+32 = 0⇒x+4x2-5x+8 = 0⇒x = -4    as, x2-5x+8 = 0 will give imagimary values of x

If log10​​​​[98 + √(x3-x2-12x+36)] = 2 , Then x =??

If log₁₀[98 + √(x³-x²-12x+36)] = 2 , Then x =??