If n is the degree of the polynomial, [2√5x³+1−√5x³]⁸+[2√5x³+1+√5x³]⁸ and m is the coefficient of xⁿ in it, then the ordered pair (n,m) is equal to (12,(20)⁴) (24,(10)⁸) (8,5(10)⁴) (12,8(10)⁴)

[2√5x3+1−√5x3𕒵]8+[2√5x3+1+√5x3𕒵]8Rationalise the polynomial,28[1√5x3+1−√5x3𕒵×√5x3+1+√5x3𕒵√5x3+1+√5x3𕒵]8+[1√5x3+1+√5x3𕒵×√5x3+1−√5x3𕒵√5x3+1−√5x3𕒵]8=28[√5x3+1+√5x3𕒵(5x3+1)−(5x3𕒵)]8+[√5x3+1−√5x3𕒵(5x3+1)−(5x3𕒵)]8=2828[[√5x3+1+√5x3𕒵]8+(√5x3+1−√5x3𕒵)8]=[(a+b)8+(a−b)8]we know,(a+b)8=8C0a8b0+8C1a7b1+...+8C8a0b8(a−b)8=8C0a8b0𕒼C1a7b1+...+8C8a0b8(a+b)8+(a−b)8=2[8C0a8b0+8C2a6b2+8C4a4b4+8C6a2b6+8C8a0b8]Thus, our expression becomes,=2[8C0(√5x3+1)8+8C2(√5x3+1)6(√5x3𕒵)2+8C4(√5x3+1)4(√5x3𕒵)4+8C6(√5x3+1)2(√5x3𕒵)6+8C8(√5x3𕒵)8]=2[8C0(5x3+1)4+8C2(5x3+1)3(5x3𕒵)+8C4(5x3+1)2(5x3𕒵)2+8C6(5x3+1)(5x3𕒵)3+8C8(5x3𕒵)4]From this, we can clearly see that the degree of the polynomial is12, henceh=12which means the option (2) (3) are incorrect.now, form, let collect the coefficients ofx12from each term.coefficient ofx12=2[8C054+8C254+8C454+8C654+8C854]=2[54×27]=54×24×24=104×24=16(104)=(20)4